Muskmelon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠪⠀⠚⠻⠛⠀⠀⠈⠱⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⢢
⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⣰⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢱
⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣽
⠀⠀⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠇
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⡟⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣴⠆⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡟⠀⠀⢶⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⠀⠀⠀⠀⠀⢀⠀⠀⣈⢤⣼⡴⠋⠀⠀⢀⠻⡃⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⣶⣦⣤⣾⣦⣸⣶⡾⠟⠋⠀⠀⠀⠀⢢⡷⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢤⣀⠀⣠⣤⣴⢩⡤⠊⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠈⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⡲⠀⠉⠉⢉⠉⠉⠀⠀⢀⡀⠒⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠊⠡⠂⠀⠐⠂⢀⡀⠀⠀⠀⠀⢀⡘⠀⡤⠶⠚⠀⠱⠈⠉⠟⠶⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡨⠕⠃⢀⠤⠂⠀⠀⠀⠊⠡⠚⠀⢀⠤⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⡀⠀⠀⣠⠔⠋⠀⠀⣀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠛⠳⣤⠆⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠔⡥⠋⠀⢀⡈⠁⠀⣠⡢⠚⠁⠀⣠⠊⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠄⡀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⣠⢋⡄⠀⠂⠀⠀⠀⠀⡠⠂⠞⠀⠀⠐⣡⠚⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠁⢰⡀⡇⣿⣼⢿⣦⡄
⠀⠀⠀⠀⢀⠜⣡⠊⢀⡔⠀⠀⠀⠜⢐⡁⢀⠔⢠⢆⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠀⡄⠀⢱⣘⣿⠿⢋⠁⠀⠈⢹⢆
⠀⠀⠀⢠⣮⠰⣅⣀⡪⢀⡠⠀⠀⢀⠞⠀⠃⠀⢁⣾⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢰⠀⠀⠀⣁⣤⣴⣶⢦⡲⣶⢾⣶⢶⡼⣟⡁⠀⠨⠤⠄⢰⡇⠀⠳
⠀⠀⢠⢧⡝⢾⡽⠛⢃⠛⠀⡠⠀⠚⠀⢀⠄⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣧⡴⠻⡏⠙⣇⣘⡆⡿⢻⣭⡿⣿⠇⠐⠀⠀⠈⠀⢠⡞
⠀⢀⢏⣤⣞⡳⢝⡫⡙⠀⡽⡄⠀⠀⠀⢎⢠⠃⠀⠀⠀⠀⠀⡄⠀⠀⠃⠀⠸⠀⠀⢈⣁⣣⣀⡇⢠⣼⣿⣿⣾⣻⣯⣿⠏⠐⠀⠀⠤⠤⢀⠎⠀⠀⠀⠀⠀⢶
⠀⣸⡈⣥⣍⢿⡏⢁⡠⠞⡜⠀⡰⠀⠀⢣⠋⠀⠀⠀⡀⠀⢰⠁⠀⠀⠀⠀⢠⢄⡴⢹⣧⡇⠈⣿⡟⣯⣼⠟⠛⠻⢋⠏⠀⠀⠄⠠⠀⣠⠋⠒⠀⠀⠀⠀⠀⠈⡆
⢠⣣⠈⠉⢿⠂⣤⣘⢇⠂⠀⠑⢡⠂⢠⡿⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠐⠁⣸⣿⢏⠉⢧⣀⣿⣷⣿⢳⣤⣤⢚⠏⠀⠄⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠐⠀⢸
⢸⡌⣋⠃⠀⣦⡘⢧⡜⡆⠴⠂⣤⠇⠾⠁⠀⠆⠀⠀⠠⠁⠘⠀⠀⠀⠖⣠⣶⠉⢟⣿⣷⣿⣿⣿⡷⣬⣛⡿⣱⠋⠀⠀⠠⠄⢠⠎⠀⢰⠀⠀⠀⡀⠀⠀⠀⠀⡇
⡇⢷⡙⢀⡽⣧⢳⡂⢻⠀⡶⠰⡉⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⡀⢿⣄⣼⣿⣿⣯⣉⣀⣹⠾⢋⠞⠁⠤⠤⠀⢀⡴⣁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣶
⣏⢺⠀⢿⣶⡶⢼⢻⠌⡆⣽⢃⠁⡾⠁⠀⠀⠀⠄⠂⠀⠀⠀⡇⢆⣴⡹⡟⢫⣀⡟⢀⣀⣬⠏⠟⢁⠔⠁⠀⠀⠀⠀⡠⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠛
⣿⡌⢰⣾⣶⡟⣶⣿⠀⢱⣾⣷⢠⢻⠂⠀⢠⠀⠀⠀⠀⡄⢠⣿⡏⢸⠙⡗⢶⣽⣶⠖⡴⠋⣠⢞⣁⣀⡀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⢸
⢻⡇⡸⣶⡎⢿⢷⣶⠀⡹⢶⡆⢾⡀⠀⠸⠈⠀⠐⠀⠠⡗⠘⡼⣵⣏⣺⣿⢏⣀⣀⣽⠗⠋⠀⠀⠀⠀⠀⣠⡎⠁⠀⠀⡤⠀⠀⠀⠀⡘⠀⡖⠠⠃⠠⠀⠀⣠⠸
⢸⠀⣽⢶⣃⠫⡷⠇⣸⢫⣿⠂⣿⡄⠀⠀⠀⠀⡈⢠⢰⡄⢰⠷⣎⣴⣯⣿⡿⡛⠉⠀⠀⠙⠃⢀⣠⠶⢊⠞⠀⠀⠀⡰⠁⠀⡀⠀⠛⢁⠰⠁⢀⢠⠃⠘⡀⠛
⠈⣤⡿⢟⡋⢘⡡⣟⣁⣾⢿⣲⠛⠁⠀⠀⡆⢸⠣⡈⢘⣳⡿⠛⠋⠉⠈⠁⠠⠄⠀⠀⠀⠀⣠⠝⠁⠔⢁⠄⡰⠃⠜⢁⠎⡰⠁⠀⢀⠎⠀⠀⠎⠁⠀⢀⠃⠀⢰
⠀⢹⡏⢋⣴⣊⠾⢭⣧⡙⠿⣹⠇⠀⢺⣀⠃⡌⠂⡷⠤⣆⠀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠊⢁⡀⢀⡴⠃⠘⠁⠋⠀⠀⠘⠁⣰⠃⠀⠀⡀⢀⠀⠀⡔⠎⢀⡀⡇
⠀⠀⠳⠛⠻⣹⠟⡑⢯⡽⡙⣹⣏⢀⠀⡜⠐⠰⠸⠧⡌⠀⠀⠀⠀⠀⠈⠁⣠⠜⠋⠁⠀⠀⠉⠀⠉⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠜⣠⠀⠀⠋⠴⠘⠇⠀⠀⠜
⠀⠀⠀⢆⣭⡻⢸⡿⢡⣅⠟⢻⠟⣾⢸⠀⡴⣴⡋⠀⠠⠤⠂⠀⢠⡴⠞⠋⠀⡀⠀⣠⠄⠀⣀⠀⣠⠔⠁⠀⠋⠀⠀⠀⠀⢀⠄⠐⠁⠀⡔⠀⠀⠀⢀⣾⡻⠁
⠀⠀⠀⠈⢷⣅⡶⣽⠦⠋⢰⣟⡄⣧⣠⡴⣶⠆⠀⠀⣀⡴⠖⠛⠧⣆⡀⠀⠀⠁⠫⢀⡀⠈⠇⠀⠀⠀⢀⡴⢂⡀⢀⠄⠀⠀⠀⠀⠀⠘⡠⠀⡀⠀⠊⡜⠁
⠀⠀⠀⠀⠀⠳⣜⣰⠃⣬⣛⡦⢻⣴⣟⣧⠬⡵⣶⠻⣇⣴⡦⠉⠩⣀⠂⠀⠤⠀⣀⠀⣀⠄⠀⠀⠖⢀⠋⠀⠉⢐⡋⠀⠀⠀⠀⠀⡁⠈⠀⡜⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠈⢧⣤⣗⡺⠀⣮⡿⣫⣜⣛⣷⡷⣺⡅⡵⢃⡰⠞⣁⡶⢄⠈⢉⠘⠀⣀⠤⠂⠀⠒⡡⠀⠀⠐⠉⠀⠀⡄⠀⠀⢀⡔⠀⢨⢆⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⠁⣦⡑⢻⡭⣯⣿⣽⡞⠛⣉⣤⣖⠉⠤⣹⢷⠃⠄⢀⡀⠀⠰⠚⠓⠂⣀⡀⣀⠄⠀⣠⢦⣞⢀⠔⠀⡠⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⡲⣼⠿⣣⣶⣤⠓⠛⢾⡏⣼⣻⣴⡖⢠⠲⠷⣋⡁⠄⠀⠡⠏⠀⠠⠀⠰⠛⠅⠜⠡⠟⠀⢸⣟⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡾⣞⣾⣻⣟⠈⣐⣋⡭⠎⣠⣯⠰⠦⠄⠉⠰⠶⡅⠠⢤⠌⠁⠀⠀⠒⠚⢒⣰⠤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠷⣿⣏⣰⢾⡽⢃⣴⠎⠟⣒⡶⢬⡥⣟⣳⠀⣠⣷⠦⠸⣿⣤⠭⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠒⠿⣥⣿⣯⣼⣯⣤⣿⣧⣿⡼⠷⠓⠚⠉⠁
⣿⣿⡿⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡠⠐⠀⠀⠈⠁⠀⠒⠤⠄⡀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣟⠛⠛⠻⢶⣦⣄⡀⠀⠀⠀⠀⣠⣤⠀⠀⠀⢀⡤⠒⠛⠻⣶⣦⡀
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⣄⠀⠘⠛⠃⢀⣴⠃⠀⣂⠴⠋⠀⡺⠋⠘⡇⠀⠀⠀⠀⠀⠀⠉⠳⣄⢄⠠⣀⣉⠉⣠⠴⢃⠎⠀⠀⠀⠀⠘⣿⢿⡄
⣺⣃⡀⠀⠀⠀⣲⣤⣿⣹⡖⠢⣄⠀⠈⠪⡙⠒⠒⠒⠉⠀⢀⡌⠁⠀⠀⡸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡱⡀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠸⣞⣿⡄
⢹⡇⠑⢄⠀⠀⠑⢎⠗⢯⣧⣄⠉⠀⠀⠀⠈⢆⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠔⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡟⣹⣧
⠘⣷⡀⠀⠑⢀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⢸⠀⠐⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡄⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠚⣿
⠀⠘⢯⡆⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢦⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡇⠀⠀⡌⠀⠀⡤⠰⡆⠀⠀⠀⠀⡀⠀⢿
⠀⠀⠀⠙⠿⣤⣀⣀⢀⣹⢲⡤⣤⣤⣤⠖⠋⠀⢰⣜⡧⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡟⢘⠀⡇⠀⢸⠑⢰⣷⣷⠀⠀⠀⠃⠀⢸
⠀⢰⡆⢀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⢀⣼⡧⠀⡀⠰⡐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢀⣇⡌⢠⠁⠀⠰⣠⣯⣟⢲⠂⠀⠀⠀⠀⣸
⠢⣀⣀⢎⣠⣴⣾⣾⣇⣉⠉⢻⣿⣶⣄⣀⠀⠀⠀⢦⣶⣀⠀⠀⢩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⠀⠀⠀⣾⢇⠁⢸⠀⠀⢀⢈⣇⣈⡉⠀⠀⠀⠀⠘⣿
⠀⢀⣴⡿⢿⣿⠀⠙⠛⠻⣿⣦⡁⠈⠹⠿⣷⣀⠀⢨⣿⣏⠀⠀⢸⣧⡀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⣿⡆⢀⠐⣠⣿⡍⠀⢸⠀⠀⠘⠏⢹⣍⠂⠀⠀⠀⠀⢹⡇
⢀⣾⣿⡗⡈⠱⠀⠀⠀⠀⠀⠉⠻⢆⡀⠀⠘⢿⡦⠀⠙⣿⣤⣠⢌⢿⣷⡀⠀⠀⠀⠀⢼⠀⠀⠀⢼⣿⢓⡤⠒⣼⡟⠀⠀⠈⠀⠀⠀⠀⠛⠈⠀⠀⡀⠀⢰⡿
⢸⣿⡙⣿⡀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⠀⠀⠻⣿⣿⡃⠸⣿⣷⡀⠀⠀⠀⢰⠀⠀⠀⣾⡇⣰⡟⣳⠟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣿⠁
⢾⡉⠓⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠛⢿⣼⣼⣿⣿⣗⢀⣾⣻⡇⠐⣷⣿⣿⣯⡿⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⣨⡿⠁
⠸⣷⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣼⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⡀⠘⡀⠀⠀⠀⠀⣄⣻⠟
⠐⠛⡆⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⢀⣀⠤⠄⠤⠬⠤⣀⡀⢄⡉⠁⠀⠀⠀⠀⠀⢠⣴⣄⡁⠀⠀⠀⢰⠀⠑⣄⠀⢀⣾⠟⠁
⠀⠹⡙⣄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⡀⠀⢸⠀⡼⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠑⠧⣦⡀⠠⣀⠀⠀⠉⠛⠚⠁⠀⢀⣴⠏⠀⠀⠈⠛⠋⠁⠀⠀⣰⣦⡆
⠀⠀⠐⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣼⡿⠃⣼⠁⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⠀⠘⠻⢦⡉⠳⣤⣀⣀⣀⣈⠤⠟⠁⠀⠀⠀⠀⠀⠀⠐⣄⠀⠈⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⣀⡼⠟⠉⠀⢸⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣝⢻⣷⡀⠀⠈⠈⣁⣠⣤⡄⠀⠒⠛⠛⠻⠖⡶⠦⣬⣙⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠀⠀⠀⠀⢸⡉⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇⢀⣴⣾⣯⠿⠮⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄
⠀⢀⣠⣴⣶⣟⡋⣉⠉⠉⠉⠉⠛⠲⢦⣄⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢲⣶⣿⠇⣼⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠈⠀⠒⠛⣷⣄
⣰⠟⠋⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠛⢦⣄⠀⠳⡄⠀⠀⠀⠄⡀⣀⡀⣀⣀⣀⣠⣬⣿⠟⠀⢇⠀⠀⠀⠀⠀⠀⠠⠤⠿⣾⣞⣸⡥⢿⡄⠀⠀⠀⠀⠀⠹
⠩⡀⠀⠀⠀⠀⠀⣚⡛⢶⣵⣷⠛⠀⠀⠀⠀⠀⠹⠀⠀⠘⢳⣄⡀⠀⠀⠈⠙⠛⣟⣛⣿⠿⠋⠀⠀⠈⠣⢀⡀⠀⠀⠀⠀⠲⠦⠠⠝⠒⠛⠀⠀⠀⠀⠀⠀⡀⠔
⠀⠈⠀⠀⠀⠀⢀⣈⣈⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠷⠿⡿⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠤⠀⣀⣀⣀⠀⠠⠀⠀⠀⠐⠁
⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⡶⣄⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⠋⠒⠐⠻⢽⡻⡾⠟⠛⠛⠛⠛⡻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠱⢸⣿⣤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠑⠮⡙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⠈⠠⢸⣿⢹⠀⠀⠀⠀⡀⡇⡀⡀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠁⡁⠊⠈⣷⢸⠀⠀⠀⡸⢋⡅⢩⢅⠳⢦⠄⠀⠀⠀⠀⠈⠃⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠐⠀⠈⠀⣿⡸⠄⠀⠀⣟⠲⡤⢠⡐⠩⠄⣭⡀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠡⠤⠈⢹⣇⡆⠀⠀⡛⠰⠆⠴⣓⢀⡋⢨⡇⠀⠀⠀⠀⠀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡏⠙⢿⢦⡁⠈⣿⠀⠀⠀⠥⠺⣉⢰⡀⢇⡍⠨⠗⠀⠀⠀⠀⠀⡉⢸⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠈⠣⡳⣝⢶⡸⣇⠀⠀⢻⣸⣼⠦⡡⠑⠃⣾⠅⠀⠀⠀⠀⢀⡇⣿⠃⡇
⠀⠀⠀⠀⢸⣷⢦⣤⣤⣼⡇⠆⠀⠀⠙⢬⡳⡍⢻⣤⣤⡈⠢⣙⣓⣋⣉⢡⠟⠀⠀⠀⠀⠀⡸⢰⣏⢹⠃
⠀⠀⠀⠀⣸⠏⡎⡄⠉⠛⠻⢷⣒⠦⡀⠀⠱⡜⠪⣝⣂⠿⠚⠛⠧⢍⣉⣀⣀⠀⠀⠀⠀⢀⣡⣿⣴⣾
⠀⠀⠀⠀⢸⣶⣇⡇⠀⠀⠀⠀⢬⢳⠻⣶⣦⣀⠓⠈⠳⠽⣄⣂⠤⢀⣉⣐⡒⠿⢗⣲⠟⣩⠔⠀⠈⠛⠻⣶⣦⣤⣄
⠀⠀⠀⠀⠸⡘⡧⡇⠀⠀⠀⠀⠈⢧⡳⣔⢮⣉⠙⠚⠳⢤⠤⣌⠉⠓⠒⠛⢛⡒⣉⠴⠊⠁⠀⣀⣠⣴⣶⣿⣁⣼⠉
⠀⠀⠀⠀⠀⢧⢇⢧⠀⠀⠀⠀⠀⠀⠉⠲⠉⣛⡲⠯⣀⡀⠀⠈⠉⠽⢲⣒⣛⡶⣲⡶⠶⠟⣛⡯⠵⠀⠀⠉⡉⣻⡿
⠀⠀⠀⠀⠀⠈⢿⢎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠋⠩⠍⠡⠖⠚⠉⠁⠀⠀⠀⢀⢞⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠈⢫⡣⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠴⣚⣵⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠿⣶⣦⣤⣀⣀⡀⠀⠀⢀⣀⣀⣐⣺⣭⣵⣶⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⠀⠀⠀⠁⠀⠂⠀⢀⠀⠀⢀⣤⠄⢀⠀⠀⣠⠶⣿⢿⠟⠉⠋⠓⠶⣄⠀⠀⠠⠤⠀⡀⡠⠂⠉⢳⣦⡀
⣿⡀⠀⠀⣤⣰⣠⠀⡀⠁⠗⠢⠤⠐⠋⣀⠊⠀⠰⠁⠈⠀⠀⠀⠀⠀⠈⠫⡪⠀⠂⠈⠔⠀⠀⠀⠀⢫⣷
⢻⠀⠀⠀⠙⢷⣿⠦⠁⠀⠀⠠⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠠⠀⠀⠀⠀⠀⠀⠀⠸⢹
⠈⢷⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⡄⠀⠀⠀⡀⡄⠀⠀⢈
⠀⠀⠙⠳⢤⣤⣵⣶⣶⠶⠚⠁⠰⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⡃⠁⠀⠸⢁⣿⣷⠀⠈
⢀⠉⢄⣠⣤⣦⡶⢶⣤⣄⡀⠀⠈⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢰⠚⠀⠀⢠⢿⣑⡃
⠀⣴⡟⢿⠈⠉⠛⠷⣄⠉⠻⣦⡀⢿⣯⠀⢸⣆⠀⠀⠀⢀⠀⠀⢀⣿⠀⡠⣾⠁⠀⠀⠈⢫⡯⠀⠀⠀⣸
⢸⡿⣇⠀⠀⠀⠀⠀⠈⠲⡀⠈⢧⠀⠻⣿⡆⣿⣧⠀⠀⠈⡄⠀⣸⠇⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⡄⢠⡏
⣿⡙⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠻⢿⣿⣿⣠⣿⣇⣰⣿⣿⠟⠁⠀⠀⠀⡄⠀⠀⠀⢠⣠⠏
⠸⣇⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡀⠤⢤⠈⡙⠛⠛⠛⠋⠉⠀⣠⣀⠀⠀⢀⠀⡀⠀⣠⡞⠁
⠀⠋⢄⠀⠀⠁⠀⠀⠀⠀⡀⣅⡌⡰⠋⠀⠀⠀⠀⠈⠙⠷⣄⠠⣀⠈⠉⠉⠀⣤⠏⠀⠈⠉⠁⠀⠰⠶
⠀⠀⠀⠲⢄⠀⠀⠀⠀⣀⠿⠋⢰⡇⠀⠀⠀⠀⠉⠑⠲⢤⡼⣷⠈⠑⠒⢒⣈⡤⠤⠤⠤⢤⣀⣓⠤⠤⠘
⠀⠀⠀⣀⣀⡉⣁⣛⣉⠁⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠉⢿⡇⣠⡾⠟⠛⠂⠐⠀⠀⠀⠀⠈⡙⢦⣄
⣠⠾⠛⠁⠀⠀⠀⠀⠈⠉⠲⢤⡀⠡⡀⠀⠀⠀⠀⠀⠀⣀⣘⣿⠃⠋⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⠙
⠁⠀⠀⠀⠐⠟⠻⠿⠃⠀⠀⠀⠙⠀⠘⠦⣄⣀⣈⣉⣿⣿⠟⠁⠀⠐⠠⠀⠀⠀⠐⠂⠙⠛⠁⠀⠀⢀
⣤⡴⠶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣦⣤⣤⣾⣿⣿⣧⣤⣤⣦⣴⣦⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠋⢴⣶⣶⠿⠶⢀⠉⡙⠛⢶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠹⠂⡉⠀⠠⠀⠈⠁⠀⠉⠠⠀⠀⣳⠂⠚⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⠷⢄⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠠⠏⠀⠰⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡍⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⡄⢀⡀⠀⠀⠈⠀⠚⠆⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠖⠀⠈⠁⠚⣧
⠀⠀⠀⠀⠀⠀⢀⣿⡻⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠒⢉⡔⢿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠙⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⢀⣀⣈⣧⣸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢁⡄⡀⠀⡄⠁⣻⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠆⣠⣽⠇
⠀⠀⠀⠀⠀⠀⠘⣷⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠁⢠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⢹⣅⡤⠀⠀⠀⠂⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⢀⣁⠠⠀⠀⠀⣛⣷⣿⠇⠀⠀⠀⣀⠄⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣆⣀⡄⠰⠛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠠⠻⣌⣭⣼⠏⠀⠀⣀⠈⠁⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣛⠶⠆⠈⢀⢀⡀⠂⣀⣩⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⢴⠠⢿⣾⠏⠀⠀⠀⣿⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣴⣟⣡⣄⠠⠎⢁⠀⡀⠀⣰⢆⠐⣤⣈⣛⢥⣤⣿⣿⡿⠁⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣆⣁⣘⡓⣠⣶⠸⣡⣟⣭⣿⣶⣿⠟⠁⠀⠀⠀⠀⣰⣉⣦⡇⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⡿⠿⠿⠟⠋⠉⠀⠀⠀⠀⣀⣠⣌⠀⣽⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣦⣤⡀⢤⣶⣶⣶⡏⣰⡶⠞⠁⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠈⠉⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⡀⠀⢀⣀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⡶⢦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡵⠞⠉⠀⡿⠋⢹⠉⠁⠆⠀⠀⠉⠛⠳⣆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣠⠎⠁⠀⢠⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄
⠀⠀⠀⠀⠀⠀⠀⡔⣼⠏⠀⠀⠀⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⢦
⠀⠀⠀⠀⠀⠀⠘⢱⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢿⠈⡃
⠀⠀⠀⠀⠀⠀⢘⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢿⣿⠆⠄⠀⢰⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⢸⢿⡦⠠⠄⢧⣃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⣼⣠⠇
⠀⠀⠀⠀⠀⠀⠘⣾⣧⡄⠀⢈⣷⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⣿⠀⠠⢠⠘⣿⡌
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢀⠨⣿⣆⠀⠀⠀⠀⠀⣇⠀⠀⢀⣰⣿⠂⠄⠣⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣮⣶⣽⣿⣆⠀⠀⠀⠀⢳⠀⠀⠐⣿⡟⣻⣾⣳⡿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣘⣿⣿⣦⣀⠄⣀⣹⡀⢘⢰⣿⣧⣿⣯⠟⠁⣀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣯⣰⣿⣿⣧⣽⣿⣿⣿⠟⣡⠔⠉⠀⠀⠀⠀⣀⠤⠶⢶⢦⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠛⠛⠉⢀⠔⠁⠀⠀⠀⠀⠐⢻⣭⢿⣶⣥⠶⠂⠠⠃⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠐⢻⣟⣿⣺⣩⣿⠇⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⡛⡒⠒⠒⠂⠀⠀⠀⠀⠐⠖⠈⠙⣿⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣤⣄⣠⣀⣀⣀⣼⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠜⠓⣄
⠀⠀⢀⠔⠀⠀⠠⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢣⡀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡸⣄
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⡹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣵⢙⠷⣻⡆⠀⢄⠀⠈⠘⡇
⡀⠀⠄⠠⠢⡀⠀⠀⠀⠉⠲⠦⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢑⠡⡪⠞⠁⠘⠜⠃⠠⠊⢲⠀⠀⠀⠀⠀⢀⠤
⡇⠀⡘⠱⣀⠇⠈⠁⠀⠐⠂⠀⠒⠂⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠖⠉⠀⠀⠇
⢁⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠲⢄
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡅⠀⠈⢂
⠀⢣⠀⠀⠆⠀⠀⠀⡀⠀⠀⢀⠀⠀⠒⠀⢠⠔⠀⠉⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡿⠀⠁⠀⠀⢀⠢⠄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠃⠀⠀⠀⣆
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⢈⠑⠤⣀⡀⠀⢀⣀⡀⠄⣒⠭⠀⠂⢄⡰⠁⠂⠉⠀⠀⢠⠀⢀⠔⠈⠀⠀⠀⠃⡀⠀⠀⠙
⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⡑⠤⡀⠀⠀⠀⠀⠀⠈⠩⣆⠀⠀⠀⠉⢢⡀⠀⠀⠐⠋⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠈⠣⡀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⣠⡆⠀⠘⡆⠀⠀⠀⠀⠁⠐⠠⠀⢀⠀⠀⠤⠐⠂⠁⢔⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢾⣄⡄⠀⠠⡠⡀⢀⢂⠀⠐⢜⢄⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠇⠀⠀⠈⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠶⠾⠾⠶⠣⣠⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣂⠠⡁⠒⣶⢤⣤⣄⣀⣀⣀⣈⣦⣄⡠⠀⡀⡀⠙⠭⣒⠄⣀⣀⡀⠀⠀⣀⡀⢤⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠲⠬⠤⠷⠦⠕⠶⠛⠛⠋⠉⠙⠳⢦⣴⣄⣲⣄⣩⣒⠀⠀⢀⡀⠉⠛⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠃⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⡄⠀⢈⠟⠰⠀⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡧⠠⠆⠰⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢰⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⣄⣆⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠰⢇⠀⠀⠈⠳⣇⠀⢀⡀⠀⠀⢤⡼⠨⠐⠁⠀⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠈⠁⠀⣀⠆⡌⠁⡏⡠⠀⠀⠀⢠⡤⠀⠀⢀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠾⠧⠤⢀⣗⠂⠀⢀⢸⡇⠀⢠⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠸⣶⢿⡤⠅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠚⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢼⣿⡟⢿⣧⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠄⣀⡘⠻⠀⠈⠉⢄⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠹⣿⣦⣀⡀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⡿⡷⠀⢹⡿⠋⠁⠀⡀⢷⣤⣎⣠⣬⠀⣠⣤⠤⠾⠛⠃⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⣄⡰⠏⠀⠀⠀⣀⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢁⣠⠀⠀⠀⠀⠀⢸⣿⣷⣿⠟⠋⡁⠀⠀⠀⢰⡯⡱⣧⣶⣦⣄⡠⢀⠀⠀⠤⠀⢀⣤⣾⣿⠿⠃
⠀⠀⠀⠀⠠⠀⠀⡀⠠⠀⢸⣷⣴⣿⡀⠀⠀⠀⠀⢸⣿⡿⠿⠶⢾⣧⠀⠀⠀⠸⡏⠀⠁⠀⠀⠉⢡⣄⣴⡟⢀⣀⢀⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠐⢀⣀⠀⠓⢻⣿⣷⡄⠁⠶⣀⠀⠀⢿⣧⡀⠀⠀⠀⠂⢀⠀⠀⡖⠀⠓⠙⠓⣶⠛⠻⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠈⢦⡀⠈⢧⡃⠀⠀⠀⠀⠈⠀⠘⠛⠳⠒⠛⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⣹⡄⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠂⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣾⣿⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣷⣼⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣠⡄⢀⠀⢘⣿⣿⣿⢧⣿⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⣿⡟⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⣀⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡮⡀⠀⠀⠀⠀⠀⣘⠀⠀⢳⢔⡰⣞⡷⣤⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣯⣅⢀⠠⠀⡐⣑⠢⢄⡹⣏⣾⢯⣸⠷⢴⡜⡂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢻⣵⡎⣐⡀⡀⡤⣆⢷⣶⣏⣟⣷⣿⠺⣲⡲⡷⣠⣄⠠⢠⡇
⠀⠀⠀⠀⠀⠈⢿⣶⣯⣇⢷⣤⣹⣒⡿⣿⣭⣽⣟⣽⣿⣞⣶⣥⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣟⣷⣷⣳⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⠏⠀⠀⠀⠀⣀⣠⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣡⣤⣴⣶⣾⣿⠿⡣⠊⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⠐⢢⠀⠛⠿⢿⡿⣛⣟⣿⡻⠭⠒⠈⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⢿⣿⠿⣿⠟⠧⠀⠉⠉⠙⠻⠿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣉⠖⠋⠁⠀⡽⠋⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠀⠀⠀⡙⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⡟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣠⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠞⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢿⠀⠃
⠀⠀⠀⠀⠀⠀⠰⣠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡁⣿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⡇⢠
⠀⠀⠀⠀⠀⠐⡷⣿⠂⠐⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⢰
⠀⠀⠀⠀⠀⠀⡽⣿⠆⠀⠄⠐⢣⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⢀⡀⣸⢡⡾
⠀⠀⠀⠀⠀⠀⢲⣾⣇⡀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠄⡀⠐⣿⢠⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡋⡀⠀⠘⣿⣄⠀⠀⠀⢀⠀⠀⠈⡇⠀⠀⠀⠀⢠⣿⠀⢀⠐⢀⣴⣟⡋
⠀⠀⠀⠀⠀⠀⠀⠱⢿⣿⢀⡅⡨⢻⣿⣤⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠐⣺⣿⡤⣀⠴⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡗⠒⣿⣿⣇⠀⠀⠀⠀⠀⣸⠀⠀⡀⢠⣿⡇⢌⣧⢦⣼⠏⠀⠀⠀⠀⣀⣠⠤⠤⠒⠒⠒⠒⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡤⣌⣻⣿⣶⣦⡐⢀⡤⣼⡄⢀⡅⣹⣿⣶⢮⣯⡞⠁⢀⡠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣄⣼⣿⣼⣧⢨⣺⣿⣿⣿⡿⠋⡤⠊⠁⠀⠀⠀⠀⠀⣀⠴⠞⠛⡛⠆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⢿⠿⠿⠛⠋⠁⠠⠊⠀⠀⠀⠀⠀⠀⠰⣯⣉⣿⠶⣬⣤⠴⠆⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠴⢶⠿⡯⢴⠟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠐⠓⠘⠓⠚⠚⠛⠉⠀⠀⠀⠀⠀⠀⣠⡞⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢒⠻⣯⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⣎⠉⠈⠋⠑⠀⠒⠂⠀⠁⠁⠉⠉⠁⠀⠀⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣷⣤⣀⢀⡀⢀⡀⢀⡀⣀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠾⠷⠿⠟⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠄⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⢡
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣛⡹⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠑⠀⠀⣠⣿⣼⣇
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⢠⠿⠿⠁⠀⠀⡀⠀⠀⠀⢀⡡⠤⠀⠀⠀⠀⠐⣤⠇⠸⢿⠀⠂⠔⣿⣟⡠⠞⣷
⠀⠀⠀⠀⠀⠀⢸⡰⡆⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⣳⡜⠀⠀⢘⡁⢠⡦⠀⡀⠀⠸⡆⡾⠀⠣⠈⠠⣼⣿⠟⠁⠀⣠⡇
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⡀⠀⠀⠚⡉⠀⠀⠤⡄⠀⡶⢰⡖⣠⡜⠃⠀⠁⠘⢇⣠⡴⠇⠽⢤⣀⠀⡇⠿⢃⣤⠶⠋⠁⣿⠀⢸⡀
⠀⠀⠠⠁⣿⣿⠟⢉⡁⢈⣯⡠⠰⡿⠇⠀⢀⣶⡇⢠⣧⣼⡅⠘⠀⣤⣼⡟⣴⣿⣁⣀⣀⣀⣤⡬⠷⠁⢴⠛⣵⠀⣀⠴⠀⢀⣎⢸⡄
⠀⠀⣇⢰⣏⡩⣶⢁⠀⡂⠀⡱⣤⠁⠸⠿⠤⠙⠁⡞⠁⠈⣧⠀⠀⠏⠙⠃⣾⣅⡀⣀⡀⣀⡄⡠⣾⣷⠈⢆⣿⠊⢉⠄⠀⢘⡁⢀⣙
⠀⠀⠸⡢⣿⣧⡜⢂⣉⠔⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠀⠀⢻⣯⣽⣯⣼⣧⠯⠻⢿⠇⠀⠀⠡⣔⠉⠀⠀⣫⡀⢀⣈⣇
⠀⠀⠀⠘⠻⢿⡿⠧⠁⠈⠔⠁⠀⠀⢀⣼⣤⣀⣀⠀⠀⠀⠀⡟⢃⠀⠀⢀⠀⠙⠶⣶⠶⠖⢒⡾⠋⠀⠀⠀⠀⠀⠀⣠⣾⣯⣥⣤⣤⣭⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣏⠉⢄⠀⠀⢰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠂⠘⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠌⡌⠐⠀⠆⠱⠈⠆⡆⠀⢘⠀⠠⠋⠰⠈⠀⠘⢠⠁⠚⠛⢠⢰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠘⠛⠛⠛⣧⠀⢰⡆
⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢠⠄⣀⠀⡀⠀⡄⢠⠀⠲⠈⠁⢀⣿⡇⠀⢠⣤⣄⠈
⠀⠀⠈⣡⡤⢠⠄⠀⣴⡇⠀⠀⠀⠀⠀⢠⡄⠀⡤⡀⢄⠀⠁⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠹⠿⠟⠀⠀⢀⣄
⠀⠀⠀⠀⠰⠈⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠰⡿⣄⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠉⠁⠈⠉⠀⠁⠡⠶⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠐⡅⠀⢠⠃⠀⠀⠃⠈⢀⣴⣷⡀⠛⠛⢁⣀⣀⡀⠀⢀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠑⢸⠘⠀⠀⠐⠰⠾⣿⡿⠆⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⢛⡉⣉⢳⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣀⠀⠀⢠⣈⣠⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠖⢳⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠙⠀⠀⠘⠖⠃⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⢀⣠⣶⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡒⠀⠀⠸⠀⠀⠀⠚⠁⠀⠛
⠀⠀⠀⠛⠛⠿⠇⠀⠛⠋⣤⡶⠀⡀⠀⠀⠈⠥⠀⠘⠂⠀⠀⢄⡐⠀⠀⠀⠸⡀⠀⠀⠀⡀⠀⠀⠛⠀⢀⢀⣀
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠻⣿⣿⣿⣄⠀⠀⣶⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠸⠇⡌
⠀⠀⠀⠻⠿⢿⣿⡷⠾⠛⠀⠀⢨⣯⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⡎⠀⠀⠀⣌⠀⠤⠀⠀⢠⡄⣬⠀⠀⢠⡆⠅
⠀⠀⠀⠈⠁⠈⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠿⠿⣿⠿⠗⠀⠀⠀⠀⠉⠀⠀⢀⣴⣄⠀⠹⠇⢀⡀⠀⢰⣿⣿⣷
⣿⡀⠀⠀⣿⣿⣿⠄⠀⠆⠀⣴⡁⠀⠀⠀⣾⣿⣷⠄⠦⠀⣾⣿⣿⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠉
⣿⣷⡀⢴⣿⣿⣿⣧⠀⠀⣼⣿⣷⡀⠀⣠⣿⣿⣿⡄⠀⠰⣿⣿⣿⡷⠀⢀⣄⣀⠺⠿⢿⣿⠿⠟⠂
⠻⠋⠁⣼⡿⣿⣿⣷⠀⢀⣼⣿⣷⡀⠀⣹⣿⣿⣿⡏⠀⠼⠿⣿⠿⠿⠄⣹⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢈
⠀⠠⠄⠀⠀⠙⢠⡄⠀⢉⣿⣿⣿⡉⠀⠛⠛⣿⠛⠛⠂⣄⢠⠘⠀⠀⠰⣿⣿⣿⠧⠀⠉⣀⠀⠐⢻⣤⡞
⣤⣤⣤⠄⠀⠀⣾⣿⡀⠚⠛⣿⠛⠛⠂⠀⠀⠉⠀⣸⡄⣏⢹⠀⣼⡆⠼⠿⣿⠟⠷⢀⣾⣿⣷⡀⠿⠛⣿
⠿⢿⢿⠀⠀⣼⣿⣿⣧⠀⠀⠉⠀⢦⡼⣆⠀⠃⢠⣿⣧⠈⠉⣸⣿⣿⡀⠀⡉⠀⠀⣸⣿⣿⣿⡇⠀⠀⣿
⠀⠸⢸⠀⣰⣿⣿⣿⣿⣇⠀⠋⠀⣾⡿⠉⣀⠀⠛⢿⠿⠓⢰⣿⣿⣿⣷⠀⠉⠀⠰⢿⡿⣷⣿⡿⠆⠀⠏
⠀⠀⣰⡀⠛⠛⢻⡿⠛⠋⠀⠀⠀⠙⠶⠿⢫⣾⣿⣄⠀⢀⣿⣿⣿⣿⣿⣇⢰⡆⢰⣿⣿⣿⣿⣿⡆
⠀⣰⣿⣷⡀⠀⡀⡀⠀⠀⣴⣶⣶⡀⠀⠀⢿⣿⣿⣿⠆⠀⠀⠉⠻⠉⠁⠀⣾⣷⡀⠀⠀⠟⠀⠀⠀⠀⠈
⠀⣹⣿⣿⡉⢰⡍⣵⠀⢈⣿⣿⣿⡅⠀⣰⣿⣿⣿⣿⢧⠠⢶⣀⡴⠃⠀⠾⢿⡿⠷⠀⢀⡄⠀⣼⣶⣶⡀
⠴⣿⣿⣿⡿⠆⠉⠁⠀⢾⣿⣿⣿⡿⠄⣹⣿⣽⣿⣽⣯⠀⣾⢿⣷⣀⣁⠀⢀⡀⠀⢠⠀⠀⢠⣿⣿⣿⡄
⣰⣿⣿⣿⣷⣄⠀⠂⢀⣾⣿⣿⣿⣷⡄⠛⠛⢻⡟⠛⠛⠃⡄⠀⣿⣿⣿⣿⣿⠀⢠⣿⣧⡀⢻⣿⣿⣿⡟
⠀⠀⢻⠁⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⣄⠀⢄⠈⠁⢀⠀⢀⣿⡀⡟⡇⠀⢸⢸⠀⣠⣿⣿⡀⠟⠛⣿⠛⠛
⠀⣧⠀⠀⠂⣰⣶⣶⡀⠀⠃⠀⠀⠀⣸⣶⣏⠁⠀⣀⢀⣾⣿⣧⠀⠁⠀⠈⠈⠘⣻⣿⣿⡛⠀⠀⣉⠀⠤
⣼⣿⣆⠀⠀⣽⣿⣿⡏⠀⣶⣶⣶⣶⣿⠋⠙⠁⢠⣿⣎⠙⠟⠉⠁⢠⣾⣦⡀⠘⠛⢻⠛⠛⠂⣴⣿⣷⡀
⠻⡿⠟⠂⢾⣿⣿⣿⡿⠄⡟⡟⠛⢻⣿⠀⠀⠐⢻⣿⣟⠂⠀⠀⢰⣯⣿⣿⣷⡀⠀⡈⠀⠀⢠⣿⣿⣿⡅
⢠⡄⣀⠀⣼⣿⣿⣿⣿⣄⠧⠃⣤⠘⠟⠀⢀⣠⣿⣿⣿⣦⡀⠀⣴⢿⣷⢿⣿⣄⢰⡟⣳⠀⣹⣿⣿⣿⣏
⢾⣽⡅⠈⠁⠀⢹⠁⠀⠀⠀⣸⣿⡆⠀⠤⠀⣰⣿⣿⣿⣆⠀⠸⣿⡿⣿⣿⢿⡿⠀⠓⠃⡄⠉⠉⢿⠉⠉
⣤⣙⡟⠀⠐⠂⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠘⠋⠉⣿⠉⠉⠃⣰⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣿⡇⠀⠀⠀⠀⠀⡇⠰⠖⠘⡸⢙⡤⢤⢐
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠋⠀⠀⠀⠀⠘⠐⠻⠈⠒⠀⠱⢎⣀⢒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⠀⠀⠀⠀⣰⣀⡀⢠⡴⡴⢤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣾⢿⣽⠀⠀⠀⠀⠩⠸⠿⣿⡖⣲⡀⠿⡗⠳⠗
⠀⠀⠀⠀⠀⠀⣴⣯⣿⠿⣷⠆⠀⠀⠀⢴⣶⢶⡂⣟⣸⣶⣶⡶⠲⠶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠐⣿⣯⣿⢿⣿⣾⠄⠀⠀⢸⡿⣢⣴⣷⣶⣶⣶⡔⠤⠖⠀⠀⠀⠀⡼⠀⠀⠀⠔⠀⡰
⠀⠀⠀⠀⠀⣼⣹⣹⣿⣿⢻⣿⣦⠀⠀⠐⣪⣼⣿⣿⠟⢻⣿⡇⠄⡀⠀⠤⠀⠈⠑⠀⢀⣴⠃⢀
⠀⠀⠀⠀⢠⣟⣻⣿⣿⢿⣿⢿⡾⢀⠀⠈⠁⠐⣿⠁⢀⡈⢻⣇⠈⡇⢀⡰⢄⣠⣦⣾⢟⠋⢀⠄
⠀⠀⠀⠀⡷⣿⣿⣿⡏⠈⣹⣗⣿⠟⠢⣤⡀⠈⡿⡬⠿⠧⣿⡇⠀⠃⠀⠀⠈⠀⠁⢸⠁⣆⠊⣀⡀
⠀⠀⠀⠀⢛⠻⠁⢘⠟⢱⡏⠛⠀⡟⢰⡄⢀⠠⡴⣦⣾⡧⠾⠭⣦⠀⠀⠀⠀⠀⠀⠈⡇⡃⠀⠈⣤⠰⡃
⠀⠀⠀⠀⢷⡤⠀⣰⠀⠈⠀⢀⣿⡟⣾⠁⣸⡇⠠⠾⠿⠷⠶⠶⠶⠶⠺⠁⠀⠂⡤⠈⠁⠀⣿⠀⢻⠞⣧
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⠄⠃⠔
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠭⢹⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⢰⠄⠀⢀⠀⠀⠠⢠⠀⠀⠀⢀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠀⠠⠉⠀⡀⠀⡄⠀⡀⠘⠀⠀⠘⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⡴⢶⡎⣀⠀⠠⠄⠀⠔⠁⠑⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⡚⠣⡀⠀⠀⠀⠀⠢⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠲⠀⣨⠡⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⣳⠡⠠⠤⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢀⠀⠀⣠⠐⠫⠁⠃⡄⠀⢠⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠠⢔⡀⠄⠀⠀⠤⠀⠌⢢⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠐⢨⢇⠜⡕⠂⠀⠀⣀⠀⠀⠈⠑⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⡱⠒⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⣀⣤⠶⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠤⠤⢀⢀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠄⡀⠂⠀⠄⠀⢀⠀⢘⡀⠀⠀⠀⡠⠀⠀⠨⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡀⡋⠁⠀⠈⠂⠀⠀⢠⠃⠀⠀⠉⠀⢤⠈⠀⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢄⠀⠀⠀⢐⢯⠀⠀⠀⠀⠖⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣾⣧⣜⢦⠀⠀⣞⠀⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⠀⠀⠀⠈⠙⢦⣠⠻⣧⣾⠇⠀⠀⠀⠀⡀⠀⠠⠂⢀⠀⠀⠀⠺
⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠇⠀⠀⠀⢰⣧⣼⡦⢿⣦⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠀⠀⠀⠀⠁
⠀⠹⢄⠀⠀⠀⡄⠀⢳⠀⠀⠀⠀⣠⡆⠀⣨⣍⣭⠖⣩⡿⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠶⠁⠀⠀⠐⠁
⠀⠀⠀⠛⠢⡈⢧⠀⠘⠀⠀⠀⠀⠉⢃⠀⠙⠛⢿⣶⣿⡇⠀⠀⠀⢀⠔⣙⣀⡚⣀⢠⠀⠀⢀⣠⡦⣉⣠⠊
⠠⡄⠀⢀⠻⣤⠿⠗⠀⠘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⢸⡷⠀⣠⡴⠟⠛⠛⠙⡁⠉⣠⣦⣴⣿⢿⠔⣠⠃
⠀⠀⠀⠀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄⣦⡀⠸⢿⠟⠢⢀⠀⠐⠗⠀⠻⠛⠋⣹⣿⡿⠀⢀⡿⠤⠄
⠀⠀⠀⠄⠈⠂⢒⣇⠀⠀⠀⠠⠀⣼⣷⠄⠘⠿⠟⢹⣶⣿⠂⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⡟⢐⠀⠈⠁
⠀⠀⠀⠀⠐⠌⣻⣿⣦⡀⣠⢤⡾⠋⠀⠀⠀⣶⣤⣷⡟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠹⣍⡻⠦⠈⠁⠐⠒⠀⠀⠈⠉⠉⣶⣤⣿⠀⠀⠀⣀⠀⠀⠠⠐⢀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⣶⡿⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠛⢠⣤⣀⠀⠀⠙⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠁⠀⢸⡟⡤⠄⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠣⣀⣀⡈⢒⠀⠐⠀⠀⠀⡀⠀⠊
⠠⠒⠂⠀⣰⠏⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⡾⠀⢀⣄⣶⣤⣀⣦⢀⡾⠁⡌⠸⠛⠉⠠⠘⠋⠀⠀⠄⠘
⠀⠀⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢈⣻⡿⠍⢻⣿⡊⠀⠀⠀⠊⠁⠠⢄⠀⡠⠒⠀⠉⠛
⠀⠀⠀⢇⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡁⣨⡴⠚⠍⠉⢐⠦⣄⠈⠑⢦⡀⠀⠤⠒⠉⠉⠑⠒
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠍⠀⢾⣦⡷⠻⣾⡿⠀⠀⠀⠁⠀⠢⣤⣞⡁
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠷⠲⢤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢬⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠄

⠀⠀⠀⠀⠀⠠⡀⠰⠀⠋⢠⠆⠔
⠀⠀⠀⠀⠲⠀⢶⡐⢘⠀⡿⣠⡞⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠠⠀⡀⠁⠈⠁⠁⢋⠴⡀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⣓⣳⣖⡈⣿⠫⣭⣛⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠃⠘⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⣰⡿⠛⢡⡾⠁⢸⣷⡄⠻⣷⣄⠙⢦
⠀⠀⠀⠀⠈⠁⠀⠂⣀⠀⠀⠁⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣿⠇⠀⣿⡟⠀⢸⣿⡷⠀⢸⣿⣄⠈⢧
⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⢄⢐⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣿⡇⠀⣼⣿⠀⠀⢨⣿⣿⡄⠀⢸⣿⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠃⠤⠂⡜⢀⡆⠈⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⡀⠀⢻⣿⠁⠀⢹⣾⣿⡟⠀⢠⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⠸⢸⣿⡷⠀⠘⣿⡇⢰
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⡀⠸⣿⣿⡆⠀⣿⡇⠀⠀⢻⣿⡿⠀⢐⣿⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⢄⠹⣿⣷⡀⢹⣿⡀⠀⢠⣿⡟⠀⡼⣣⠊
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠿⣷⣄⢻⣧⡀⣸⣟⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠈⠁⠀⠀⠀⠀⠀⠰⣄⠖⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠉⠀⢁⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⡠⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⣈⠀⠀⢀⣀⠴⠊
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⡀⠀⢀⠖⢅⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠈⠀⠘⠁⠰⠀⠀⠀⠀⠀⠀⠀⠋⠉⠏⠁⢀⠆
⠀⠀⠀⠀⠀⠑⠢⠤⣀⣀⠀⠀⢀⣀⣀⣀⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⠿⠯⢠⣾⣧⡀⠐⠀⠀⣾⠁⢨⡷⠀⣴⢒⣦⠀⢉⡀⢰⢿⠂⣰⡿⣛⠻⣇⠀⡞⠀⠈⢳⠋⠀⠙⡆
⠀⠀⠀⣰⣿⡟⣿⣷⡀⠀⠀⠹⢤⣀⡀⠀⢻⣌⣉⢰⠫⣽⠂⠀⠀⠹⣷⣭⣾⡏⠀⠳⡀⠀⢺⠀⠀⡸⠃
⠀⠀⣴⣿⣷⡅⣥⣿⣿⣄⠀⣶⠆⢨⠟⣉⠉⠉⡉⠙⢳⡀⠀⠃⠀⠐⢶⠭⠶⠆⠀⠀⠙⢦⣸⣠⠞⠁
⠀⠈⢉⣽⡿⠇⡿⣿⣏⠉⠀⡀⠀⠘⠦⠿⠀⠀⣉⣀⣰⣧⣄⣀⣀⡘⠻⠖⠿⠃⢀⣤⡀⠀⠙⣡⡶⣤⡀
⠀⠠⠾⢿⣿⡆⣾⣿⡿⠧⠀⡁⢀⠀⠀⣀⣶⣀⠙⣿⣿⣿⣿⣿⡿⠟⠀⠄⠀⠀⠈⠛⠃⠀⠸⣕⡿⣫⡇
⠀⠀⣠⣿⣯⡃⢋⣿⣷⡀⢸⣎⣹⡁⠐⣺⣿⣗⠂⢸⣿⣿⡟⠁⠀⢠⡄⢶⢦⣤⠀⠸⣿⠟⠀⢉⣉⠉
⠀⠐⢛⠛⠛⣷⡟⠛⠛⠛⠈⠑⣋⡁⠀⠀⠛⠀⠀⢸⣿⣿⣧⠀⢸⡗⢠⣶⣦⠐⣷⠀⠀⠀⣰⢿⣿⡷
⠀⠀⣉⠠⡄⢉⠁⠀⣠⡀⠠⣾⣿⣿⣆⠀⠀⠙⠀⢸⡿⡟⡿⣧⠘⢫⡄⣩⣡⣬⠋⠀⢼⣿⣇⣠⡿⠃
⠀⢠⣭⡷⢳⣯⣄⠘⠿⠏⠀⠘⢿⣄⣸⣿⣯⠄⢀⣿⡁⠀⠀⣽⣧⠀⠀⠉⠁⠀⠀⠄⠀⠀⠉⣉⠀⢠
⠀⠀⠴⢋⡏⠳⠀⠀⢀⠀⠀⢀⣀⣉⣉⣉⣤⣶⣿⡿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣦
⠀⠀⠀⢠⣤⡄⠘⠁⠘⢷⣾⣿⣿⣿⠿⠻⣻⣿⡃⠀⢐⣻⣿⣿⡿⠛⠉⢀⣿⠏⣿⡆⢠⣾⣯⣩⣿⣷⡀
⠀⢰⣿⡟⣙⢻⣷⠄⠀⢸⣿⣿⣿⣧⣀⢀⢸⣿⣷⣦⣷⣿⡿⠋⠀⠘⠃⢸⡿⠀⣿⠇⢀⣼⣿⢙⣿⣧⡀
⠀⠀⢽⣧⣭⣾⡏⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣁⡤⢤⣀⠀⣰⡞⠁⣴⠟⠀⠀⣼⣟⠛⣿⣇
⠀⢰⣶⣭⢀⣭⣶⡆⠀⢰⣿⣿⣿⣿⠋⠉⠀⣠⣀⠀⡼⢃⢮⣷⡂⢧⠈⡀⠀⢡⡀⠀⠈⠉⠉⡿⠉⠉⠁
⠀⠈⠻⠿⠿⠿⠛⠀⢠⣿⢣⣿⡟⠁⠖⠀⠀⠛⠋⠀⠸⣆⡛⢟⣂⠏⠈⠁⣰⣿⣿⡄⢀⡄⠀⠠⡞⢳⠄
⠀⠀⠠⠀⠀⠒⣠⣴⡿⠃⣼⡟⠀⣰⠚⣶⣴⣾⣶⡀⠀⠀⣍⢉⠀⠀⠀⠐⣿⣧⣾⡟⠂⠀⢀⡀⢉⠉
⠀⢠⡶⣲⢶⣰⡿⠋⣠⣾⠟⢁⠀⠹⣾⣿⣿⣿⡿⠀⠐⢶⡿⢻⡷⠂⠀⠰⣿⣧⣾⡿⠂⠐⠶⢟⡻⠶⠂
⠀⠸⣞⣿⣳⠇⠀⠀⡿⠋⠐⣏⣱⠀⠘⢿⡿⠋⠀⠆⠐⠛⡿⢿⠛⠃⠀⠰⠛⢧⡾⠿⠂⠐⢋⡶⢾⠙
⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠻⢀⠘⡀⠃⠀⠶⠧⠊⠃⢡⡴⠀⠶
⠀⠡⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⠁⠀⠠⣤⢠⣆⣃⠦⢯⢡⠑⣄⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠉⠓⠁⠈⠀⠀⠘⠑⠀⡄⠉⠉⢠⠀⠊⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠩⠁⠀⠒⠐⠊
⠀⠀⢠⡀⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡀⠡⠀⠀⠀⠂⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣦⢤⡶⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⡨⠂⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡤⠔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠒⠒⠒⠒⠒⠒⠤⠠⢤⣀⡀
⠀⠀⠀⠀⠀⢀⠖⣡⠴⠖⠒⠒⠒⠒⠒⠲⠶⠶⠶⠤⠤⣤⣀⣀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⣴⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣀⠀⠱⣄
⠀⠀⠀⣸⠏⢀⣀⣠⣤⠤⠤⠤⠤⠤⠤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢣⡀⡏⢧
⠀⠀⠀⣯⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠦⣄⠀⠀⣧⡇⣸
⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡙⣾⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠄⠤⠤⠤⣄⣀
⠀⠀⠀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣏⢻⠁⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⢀⣀⡀⠀⠀⠈⠑⢄⣀⡀
⠀⠀⠀⠸⣄⠉⠓⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⢁⡟⢸⠎⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⡀⡴⠖⠉⠉⢉⡉⠉⢶⡀⠀⠈⠳⣇
⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠋⠛⠋⠉⠉⠉⠁⠀⣠⠞⢀⠏⠀⠀⠀⣠⠔⠉⠀⠀⢀⣴⠞⠀⠀⠀⡄⡘⠸⠸⠈⡀⢃⣄⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠈⠙⢽⣓⠲⠤⠤⢤⣤⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣠⠴⠚⣁⠴⠋⠀⠀⣠⠞⠁⠀⠀⣠⡶⠋⠀⢀⢀⠓⠰⠀⠆⠈⢴⠌⠊⠀⠌⢣⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠤⠤⠤⠤⠬⠭⢉⣉⣉⡭⠥⠤⠒⠋⠁⠀⠀⠀⡼⠁⠀⠀⡠⠾⠂⠀⠐⠂⠢⠠⠀⠁⠠⠶⠋⠁⠐⠀⠭⠅⡸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⡾⠃⢠⠀⠉⢀⠀⠃⣀⣴⠕⠁⠠⡀⠌⠠⠁⠁⣰⠇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠋⠀⠂⠀⠀⠄⢀⠄⠊⠋⢀⠀⠒⠐⠀⠂⠀⢀⡾⠁⠀⠀⡠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣦⡉⠄⠉⠀⡒⠕⠁⠀⠄⢠⠁⡄⠈⢀⣤⠖⠋⠀⠀⢀⢔⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠩⢔⡀⠡⠊⠠⠀⡌⣈⠀⠂⠀⢠⡴⠊⠁⠀⠀⣠⢔⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢻⡄⠌⠐⠐⠂⢀⣠⠔⠛⠁⠀⠀⢀⠔⡪⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠁⠙⠂⠒⠋⠉⠀⠀⠀⢀⠠⣊⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⣀⣀⠀⠀⣀⠠⢔⣪⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣍⠢⡀
⠀⠀⠀⠀⠀⢀⣤⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣷⡥⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⣿⣧⣑⢎⣉⠲⠄⠀⠀⠀⠀⠈⢻⣽⣞⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡫⠢⠀⠀⠀⠀⠀⠀⢻⣝⠞⣮⡀⠀⠀⠀⠀⠀⠄⡌⢹⠑⡆⠙⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠤⠹⣄⠀⠀⠀⣿⡏⠈⢀⠀⠄⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣼⢻⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣠⠀⠠⠀⠀⠘⣿⡘⡄⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡧⠇
⠀⠀⠀⠀⠠⡀⠀⠄⠀⠀⠀⠀⠀⠈⠻⣿⣆⠃⠂⠀⠀⠹⠅⠡⣳⢸⠀⠀⠀⠀⠀⢀⠄⠆⠴⢤⠀⠀⠀⠀⢿⢀⠀⡍
⠀⠀⠀⠀⠀⠃⠓⠰⠰⠛⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠘⠂⢃⢸⠀⠀⠀⠀⠀⠀⠠⣤⢆⠀⢛⠀⠀⠀⣾⣞⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠈⠳⣸⣿⠀⠀⠀⠀⠀⠄⠀⠚⠂⢀⠞⠀⠀⠀⣿⢿⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢤⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡇⠆
⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣹⢀⡇
⠀⠀⠀⠀⠀⢈⣀⠈⢳⠀⣰⠗⠛⠛⠢⡀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⢨⣽⣟⠸⠈⠃
⠀⠀⠀⢠⠀⠁⠀⠀⠺⣆⣧⠞⠉⠒⠄⡔⠀⢸⣿⠁⠀⠂⠀⠀⠀⣆⠀⢀⣠⣤⣀⠉⠀⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⢸⡀
⠀⠀⠀⠈⢠⠀⡵⠊⠉⣩⠳⡄⠀⠐⠜⠀⠀⣼⣿⠀⠈⠀⢀⡐⠋⠀⡨⠚⠁⠀⠀⠹⡔⡄⠀⠀⠀⠀⠘⣇⡏⡟⠀⠎⠁
⠀⠀⠀⠀⢲⠆⠀⠀⢠⠛⣆⠈⠒⠀⢘⠀⠀⢿⡇⠀⠀⠀⡀⡆⢴⡼⠁⠀⠀⠀⠀⠀⡗⠀⠂⠀⠀⠀⠀⣳⠁⠲⡗⣼⠃
⠀⠀⠀⠀⢻⠀⣰⠀⠘⠀⠘⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⣹⠀⠸⡇⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⡻⠌⡇⡟
⠀⠀⠀⠀⠀⣠⡏⢠⣦⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣈⡀⡁⠇⡜⠀⠀⠀⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠻⠷
⠀⠀⠀⠀⠀⠈⢡⡾⢱⣄⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⣋⠀⢣⡄⡇⠀⠀⠀⠘⣷⡦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠇⠀⡈⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⣏⠰⣸⢁⡇⠀⠀⠀⠀⠈⣽⣌⢢⣀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣇⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⣏⡼⠁⠀⠀⠀⠀⠀⠨⣿⣳⣬⠀⠵⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⣄⠃⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⠛⡟⣻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣹⡿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢏⡶⣿⣾⣿⠿⠿⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣟⣋⣅⣀⣤⣤⣬⣽⣭⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠿⢿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠐⠀⠀⠀⠀⠀⠀⠉⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⡀⠠⠀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠀⠀⠀⠀⠂⠀⠀⢀⠄⠀⠀⢀⣐⠀⡀⠀⠣⣦⡀⠀⠀⠀⠛⠀⠄⠂⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠈⠀⢁⣈⠀⠁⠀⠄⠠⠇⣁⠘⢃⣝⠯⢘⠆⡀⠀⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡃⡃⠀⡀⠀⠀⠀⠠⠈⠰⡀⣄⢈⠘⣸⡋⣴⣩⢏⠘⣽⡇⡀⡂⠜⠴⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠣⠂⠳⢀⡀⢈⠑⠀⠗⡀⢉⡒⡒⡀⡇⣷⢅⠻⠼⢏⢨⡁⡛⡀⣂⢁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⢯⠂⣀⣁⠀⡄⢰⠸⢗⡈⠟⠟⣟⣄⣏⢸⢘⡻⢟⠠⠴⢉⡙⣌⢢⡐⢆⣀⠄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⡝⣛⡂⣡⠀⡖⠹⡅⠆⣷⣡⢛⣈⣉⣻⣷⢟⢻⡶⣦⠵⣦⢈⣒⢢⣽⣴⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣶⡙⢿⢈⣧⢿⡷⠳⠘⣼⡉⢫⠹⣾⣻⣿⣾⣿⣿⣿⣾⣾⡻⣐⣧⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡿⣯⢹⣿⣧⣶⣃⡳⢉⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣖⣻⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⢺⣿⡇⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⢋⡀⠀⢠⣄⣖⣤⣾⣿⣯⡙⢀⠜⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⢿⣾⣿⡟⡛⠙⠋⠛⣛⡧⣯⢻⣽⣙⣍⣴⣳⣿⣆⠳⠿⠋⢉⡡⠖⠁⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⡇⠉⠹⣆⠀⠈⠙⠻⠯⣿⣛⣉⣉⣋⣽⡧⠥⠴⠂⠉⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣵⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⠤⣤⡤⠤⠤⠖⠚⠉

⠀⠀⠀⠠⢀⠀⠀⠀⠀⡀⠀⢀⠀⠐⢠⡄⠀⠀⠀⠠⣸⣀⠤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢄⣸⣠⠄⠀⠀⠀⢀⡄⢂⠀⡀⠀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠱⠘⠀⠀⠀⠠⠄⣻⠄⠑⠆⣲⢒⡐⠂⠀⠐⠛⡝⠒⠀⠈⠒⣀⢀⠰⢀⠄⡠⠎⠀⠐⠊⡍⠓⠀⠀⠀⢂⡚⢖⠀⠎⠡⣞⠠⠄⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⢈⡁⠆⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠐⠀⠀⠈⠁⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠀⠀⠀⠘⢘⡠⢣⢜⡳⠜⠀⠁⠁⠈⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠀⠀⠄⡹⠃⡭⠀⠀⠀⢀⠐⠑⠠⠍⠂⠑⢦⡀⠀⠀⠨⢐⠟⡠⠀⠀⠛⠀⢀⠀⠀⢠⠀⠀⠀⠀⡀⠠⠄
⠀⢀⠀⢿⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠂⣼⠆
⠀⠀⠂⠠⡄⠀⠀⡀⠀⠀⠠⡇⠀⠆⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠆⢨⠅⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠤⠢⠀⢠⠀⠀⠐⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⡠⠀⠔⠤⠤⠄⠀⡄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠒⠀⣷⠀⠀⠀⠑⣄⠀⣀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⣀⠌⠀⠀⠀⣴⠀⠔⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠒⣀⠋⠰⠀⠀⠙⠛⠀⢣⠆⠀⠀⠀⡄⠀⠀⠐⡞⠂⠛⠊⠀⠀⠒⠘⣀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⡄
⠀⠀⠀⠀⢤⠘⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⠘⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣠⠁
⠀⠀⠀⠀⠀⡀⠊⢠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠤⠑⢂⠄
⠀⠀⠀⠀⠀⢀⠐⠆⢀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠘⠢⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠔⠛
⠀⠀⢠⡄⠀⠀⠀⠉⡈⠂⡑⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠐⢃⡈⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤⠄
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠄⠄⠡⠄⠤⠀⠀⠠⠀⠀⠂⠀⠀⠀⡈⢀⣀⠀⠄⢂⠀⠀⠀⠀⣀⡰⠤⡀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠃⠀⠀⠀⠀⠂⠀⠄⠀⠀⠤⠠⠤⠀⠠
⠀⠀⠀⠐⠈⢀⠂⠀⠀⠀⠀⠘⢣⣽⡀⣁⢒⢡⡤⠭⠒⢠⠊⠉⠀⠀⠀⢉⣇⣀⠟⠀⠀⠀⠘⡙⡄⠐⠭⠤⡌⠐⣀⢀⣼⣔⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠐⠋⣕⠉⠉⠀⡃⠠⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠘⡉⢢⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⢲⢺⠀⡉⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡗⢒⠢⠔⠂⠀⠀⠀⠠⡄
⠀⠀⠀⢈⣰⠀⠀⠀⠀⠂⠒⢋⠁⡈⠐⠀⠀⠀⠀⠀⠀⠀⠗⠔⠃⠠⠄⠀⡀⠀⠀⠃⠘⠀⠃⠌⠀⠀⠀⠀⠀⠀⠈⠐⢉⠀⡉⠒⠀⠂⠀⠀⠁⣦⠀⠆
⠀⠀⠀⠈⡃⡄⠀⠀⠀⠈⠄⢨⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⡁⠠⠁⠀⠀⠀⢁⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠃⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠀⠐⠀⠀⠀⠄⢰⡈⠣⢀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠓⡄⠀⠀⠀⠀⠐⠂⢲⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⠀⠀⢀⠞⠁⠃⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣰⣿⡷⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣛⣿⣿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡧⠄⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣰⠃⠈⠉⠐⠀⠀⡀⠀⣀⠠⠂⠀⠀⣰⡖⠀⠀⠀⠀⠘⡦⠙
⠀⠀⠀⠀⠀⠀⡀⢯⠀⠀⠐⠀⣠⣤⠀⣿⣤⠤⠂⣤⠄⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢉⡔⡎⠆⠕⠛⠓⠾⢿⡀⢰⣿⡄⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⡀⠈⠀⠀⣷⡶⠠⠀⠀⠀⠀⠒⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢀⣀⠀⠈⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⠈⠑⠉⠿⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⡈⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠊⠐⣷⣄⡀⠀⠘⠀⠀⡐⠀⠀⠀⠀⠀⡠⡤⠂⡠⠗⣼⣧⡄⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣸⡿⠆⣹⠟⠉⠀⣀⣶⣾⣷⣿⣷⣦⡽⠟⠛⠘⠁⣴⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠂⠀⠀⠀⠀⢼⣿⣿⣷⠶⠋⠀⠀⣤⠿⠏⠉⠉⠀⠀⠀⠀⠀⠀⢠⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠛⢻⣶⣿⡀⠀⠀⠀⢺⣿⢿⣤⣆⠀⠀⠀⠁⠀⠀⠀⠀⢀⣠⣤⡠⠤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣏⠳⢄⠀⠈⢿⡀⠀⠀⠀⠂⠀⢀⠀⢄⠀⢤⠾⠿⠿⠿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠑⡀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠻⣿⣷⣴⣿⡀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠺⢤⣀⠀⠀⠀⠉⠛⢻⣧⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠶⢦⣄⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⢤⣤⣤⣾⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⢛⣯⣭⢟⡻⢟⣿⢿⢿⡿⣟⠿⢝⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⢀⣴⠞⠉⣠⡖⢋⣴⡟⠡⣟⠀⢷⠀⡙⣦⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⢠⣶⠟⠉⢀⣼⠟⠀⢸⣿⠀⠀⣿⠁⠀⢷⡀⠈⢻⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠁⢠⣠⡟⠁⠀⣰⡿⠇⠀⢀⣿⠃⠀⢠⣏⠀⠀⢸⡇⠀⠀⠹⡄⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⣾⠋⠀⠀⣾⡿⠀⠀⠀⣸⠇⠀⠀⠀⣿⠀⠀⢠⣿⡄⠀⠀⣷⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⣼⡏⠀⠀⢰⣿⠇⠀⠀⠀⣿⡗⠀⠀⠀⣹⡇⠀⠰⢿⡃⠀⠀⢘⣿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡟⠁⠀⢀⣸⡇⠀⠀⠀⢀⣿⠀⠀⠀⠰⣿⡇⠀⠀⢸⡇⠀⠀⢨⣿⠀⠀⣸⣇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⡁⠀⠀⣿⣿⠁⠀⠀⢀⣾⡟⠀⠀⠀⠀⣿⡅⠀⠀⠸⣿⠃⠀⠀⣿⡇⠤⠘⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢠⣿⠁⠀⢸⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⠃⠀⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⢘⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣠⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣿⡀⠀⠈⣿⡇⠀⠀⠀⠀⡿⠗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⡇⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢸⠷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⣀⠀⠀⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣶⣦⣤⣤⣠⣤⣤⣤⣤⣶⣾⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⡶⠶⢶⢶⡶⠶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⣶⢶⠶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡯⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣙⣳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡙⠿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣋⣤⣴⣿⣷⣆⠈⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠟⢻⣿⠿⣿⣿⣿⣿⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣠⠴⠛⠃⣤⣾⣿⣿⣿⣬⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣧⠄⢀⣴⣿⣅⢀⣿⣿⣍⡻⡟⣳⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢆⢀⡷⣼⣿⣿⡿⠟⢁⡰⠎⣩⣿⣿⠏⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢿⣿⢿⣿⣿⡟⠉⣃⢲⡛⠛⠛⠻⢆⣈⣤⣤⠴⠋⣹⠇⠀⠀⢀⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢀⢉⡼⠋⠁⢠⣾⣿⣯⠝⢶⡤⡴⠾⠿⠟⢽⢳⣾⣥⣤⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⠞⠛⣿⡀⢀⡀⣀⣾⣿⣿⣿⣶⣤⣤⣤⣷⣶⣶⡘⣟⣿⢿⣿⠿⢿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣁⢀⣤⠂⠀⢀⣨⣷⣨⣿⣿⣿⣽⣿⣿⣿⡇⠀⢹⣿⡟⠿⡿⢧⣿⣶⣤⣴⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣒⠉⠙⠓⠲⠧⢬⣁⠛⠉⣫⣼⣄⡠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠛⢹⢿⣻⣽⠟⠋⢱⣾⠿⢿⣦⡽⠟⠛⠿⣿⡷⣶⡄⢠⡼⢋⢀⡀⠀⣠⣶⢶⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡂⣀⠠⣦⠰⠟⠉⠀⣀⣠⣾⣿⣄⣼⣿⣖⠶⢤⣤⡬⢿⣶⠊⠁⠙⠿⣿⣿⣶⣟⣁⣾⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣉⢩⣅⠀⠀⠘⣧⡀⣠⣾⠟⠛⠋⣠⣦⠀⠛⢿⣦⣆⡀⠀⠀⠙⠿⣷⣠⣤⣀⠈⠉⣉⠉⣭⣁⣴⣶⣾⠇
⠀⠀⠀⠀⠀⡸⢸⣿⣿⣦⡆⠀⠙⠣⣾⠟⣿⡷⢀⣷⣷⡟⠾⠁⣀⣴⣿⠧⣿⣷⡀⠀⠙⣿⣿⠂⠀⠀⡖⠉⢻⡟⣿⣿⣶⣿⣶⡏⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠐⣷⣾⡿⢣⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⢻⣿⣥⣿⠒⢿⣿⡇⠀⠀⠈⢿⡿⣿⣇⠰⢲⠞⠀⠀⠙⢿⣇⡁⠀⠀⠀⠀⠀⣠⡄⢰⣞
⠀⠀⠀⠀⢀⡿⠙⢱⡟⠀⣴⣶⣶⣶⠀⣠⣴⠿⠋⢀⡰⣷⣾⣿⣿⠿⢿⠦⢾⣿⣷⣶⠀⢀⠈⠙⠻⢿⣿⣛⢿⡷⢦⣄⣠⣈⢉⠓⢦⣤⣤⣾⢣⢿⣼⣿⡇
⠀⠀⠀⠀⢸⠃⠀⡾⢸⣿⡘⣿⣿⣿⡟⢉⠀⠀⣰⣿⣷⡸⣿⣷⣿⣤⣴⣄⣴⣿⣟⣻⣾⣿⡆⢰⣶⣾⣯⠉⠳⣄⠸⠟⠛⠛⢾⣿⣤⣦⣤⣿⣿⡜⠛⡿⠤⠴⠂
⠀⠀⠀⠀⢸⡆⢸⡇⠀⣿⣧⠹⣿⣿⣿⡘⢷⣿⠟⢛⣉⢷⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⣿⠇⣾⣿⣿⡟⢀⡼⠋⣀⣀⠀⠀⠀⣽⢻⡽⠿⣿⡍⠀⢸⠷⠿⠂
⠀⠀⠀⠀⢸⣇⠈⢷⡖⠛⡿⠃⠉⣀⣀⣰⣞⢳⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⢀⣤⣤⣄⢸⠟⠀⠿⢿⣿⣧⣾⣵⣿⠟⠻⣿⡆⠀⣷⢰⣇⣴⡟⣠⢆⡇
⠀⠀⢀⡴⠾⣷⡀⠈⢿⡾⣧⣴⣿⣿⠋⠉⣿⣿⣿⣿⡇⠀⠀⠸⡏⢿⡇⣰⠿⠋⠉⢻⡟⠶⠦⠶⣦⣿⣿⣿⣿⠀⠀⠀⢹⣿⢠⡷⠖⢛⣫⣾⣡⣾⣀⡀
⠀⠀⠈⢰⣿⣿⠧⡀⢨⢷⣿⣿⠷⠛⠀⠀⣸⣿⣿⡏⠤⠀⠀⠀⣿⡘⣹⣿⠀⠀⠀⣼⠀⠁⠀⠀⣜⢹⣿⠟⣿⠄⠰⠆⣼⣾⣯⠶⢒⣻⣿⣟⣥⣤⢀⡉⠁⣀
⠀⠀⠀⠀⠉⠃⠀⢻⣿⣼⣟⢣⣀⠐⣠⢤⣿⣿⣿⣿⠔⣄⠶⢰⣿⠇⢻⣿⠣⡜⠃⠻⡇⠶⠀⠀⠉⣻⣟⢦⡀⠶⣤⠴⠂⣠⢿⣾⡟⠋⢠⡅⠈⡿⠏⠛⠃
⠀⠀⠀⠀⠀⣼⢻⡏⠙⢯⠙⠿⢿⣯⣤⡞⠁⣉⣿⡀⠀⠀⠑⠉⠉⠀⣸⡈⣳⣶⣶⡾⠿⢆⠰⡶⠚⢿⣿⣿⣿⣶⣦⣀⠶⠋⣀⠬⠛⢁⡾⠶
⠀⠀⠀⠀⢰⡇⡀⠃⣀⢈⣷⣀⣀⠈⢩⡙⠚⠻⠿⣷⣤⣀⣀⣀⣄⣰⣿⣿⣯⢿⣿⣇⢀⡜⠉⢱⣄⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣸⣧⣄⠀⠈⡄
⠀⠀⠀⠀⣸⢟⣡⠋⣹⣿⣿⣿⡿⢣⢸⡏⡷⣶⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⡧
⠀⠀⠀⢀⡾⢹⡇⠀⢿⢻⠝⡏⠀⠀⢸⡇⡇⣿⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠆⢶⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣠⡄⣲⠴⢷⠀⣸⡿⢥⣠⠔⠋
⠀⠀⠀⢘⣷⠟⢳⡀⢀⡟⣰⠀⠀⠀⠘⠃⠗⠿⢸⡏⢸⡇⢸⡇⢰⡆⡆⠀⣿⠀⠀⢼⠐⡆⣷⠁⣷⠛⣤⣿⢸⣿⣿⠷⠟⠃⠈⢠⡏⠀⢠⡗
⠀⠀⠀⢸⡏⠀⢸⣿⣼⠁⠈⠉⠛⠲⠦⠤⣤⣀⣀⡀⠈⠁⠈⠃⠈⠃⡇⠀⠙⠀⠀⠚⠚⠃⠛⠀⠉⠀⠉⠀⠀⠀⣀⣀⠤⠤⠒⠉⢷⣠⠟
⠀⠀⠀⠈⢿⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢴⡦⠶⠶⠖⠙⠃⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⡤⠔⠀⠛⠲⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⢀⠔⠀⠀⠈⠀⢁⠐⠚⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠈⠀⠐⠁⣠⠄⠀⣠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⢀⠀⠀⡀⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⢠⣿⠟⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣄⡐⢁⠄⠀⡐⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⢥⢴⣦⣼⣦⠿⠋⠀⠦⠀⡎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣯⡿⡥⠏⡔⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⡋⡁⢙⣼⣾⣽⣾⡟⠀⠀⠀⠀⠌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⣯⡙⠟⣁⠶⠃⡀⠀⠪⠃⠀⠀⠀⠄⠀⠀⢀⠀⣔⣾⡉⢻⣾⣽⠟⠛⡛⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠢⡄⢋⡲⣿⢅⡠⣐⢠⡏⠀⠀⠈⠀⠀⠀⠀⢀⡼⢯⣄⣷⣾⣟⣿⡾⡉⠁⢀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡼⢁⣾⢧⡙⠀⣄⡋⡄⠀⠀⠀⠀⠀⠀⠀⢐⣉⠦⣼⠿⣯⣉⡹⠫⠋⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢲⡃⣼⣿⣼⡇⢰⣿⢰⡇⠀⠄⠀⠀⠀⣼⡖⠻⣏⣶⣵⣶⠎⡩⠈⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣷⣟⣿⠇⣸⡏⣸⠀⠐⠀⠀⠀⠆⢩⠷⣷⣿⣍⡥⠗⣉⠀⠈⡁⡴⠁⠀⡀⠀⠀⡠⠀⠀⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿⠆⢋⡖⣹⣧⡟⠀⠀⢀⡄⠸⣧⡿⠗⠛⠛⠃⠀⠀⠀⡰⢊⠕⠀⠄⠀⡀⡀⠀⠠⠂⠠⠂⠀⠆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⣶⣟⣿⣝⣿⡇⠐⢀⢂⢰⠢⠏⠠⠀⢀⡀⢀⡤⠖⢈⠄⠠⠂⠀⠀⠀⠀⠠⢃⠀⠀⠀⢀⠚⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⢷⣞⣻⠾⣷⡴⠀⣠⡜⠉⠠⠀⢀⡤⠄⠉⠀⡀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠈⢠⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⢿⢁⡾⣆⣦⡖⢖⣀⣀⢖⠈⠷⠀⠀⠀⠁⠄⠈⠀⠀⠠⠂⠀⠄⠀⠀⠀⠀⠄⡠⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡿⠋⣼⣿⡹⢿⡯⣝⡻⠡⠜⣠⡈⠓⠂⠀⠁⠀⠐⠀⠀⠐⠀⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⣻⣿⣿⠛⢡⣶⣌⣾⣳⠁⣠⡄⠀⠐⢀⠄⠀⣀⡀⡴⣠⠂⡜⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⠉⣘⡿⢃⣎⠭⠓⠠⢄⠀⡀⠂⠀⠄⠠⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠼⣟⣱⣾⣙⣶⣺⣿⣄⣴⣷⠼⠷⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⢻⡆⠀⠾⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠸⠿⣿⣿⣿⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠘⡏⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠉⢠⠶⠢
⠀⠀⢠⣿⣀⡶⠀⠀⠀⠀⣀⣀⠀⠀⠈⠙⢦⣄⣤⠷⠤⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠐⣿⣷⣀
⠀⠀⣿⣿⣿⣀⣾⡵⠶⢿⣍⣩⣍⣉⣉⠈⠉⣁⠀⠀⢀⣴⣾⣷⣾⣯⣭⣉⡻⠭⠒⣀⠀⠀⠀⠀⠀⡞⠀⠀⠈⢻⣿⠆
⠀⠀⣿⡟⠛⠓⠀⠀⠀⣾⠯⠉⠓⠦⣽⣿⣿⣁⡀⣤⣿⣿⣿⣿⣷⣧⣢⠉⠙⠾⣇⠙⢷⠀⠀⠀⠀⡇⠀⢀⣀⡀⠙⠃
⠀⠀⣿⢯⡑⢦⣀⢀⠀⠙⢷⣤⡀⠀⠀⠈⠘⢿⣿⣿⣿⣿⣿⣿⣧⣄⡙⠓⢷⣶⡈⢳⡀⠀⠀⠀⠀⣿⡀⣿⣿⣥⣶
⠀⠀⠹⣎⠻⣶⣭⡐⠝⠀⠀⠉⢻⣷⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣘⠂⢰⣿⣿⣄⢻⡄⢈⠀⣾⡿⢿⡟⣿⣿⣿
⠀⠀⢀⣬⣷⣶⣭⣝⢃⠕⠂⠀⠈⢻⡏⠙⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣯⣿⣞⣷⣾⡿⢿⣾⣿⣿⣯⣛⠓
⠀⠀⣿⣿⣿⣿⣿⣿⣦⣄⠀⢀⠀⠀⢿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣾⢽⣷⣬⣵⣿⣿⣿⣿⣿⡀
⠀⠀⢽⣿⣿⣿⣿⠿⣿⠏⠸⠛⠓⢂⡞⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣶⡶⠛⠻⠛⢻⠿⠿⠿⢭⣉
⠀⠀⠀⢙⣿⣿⣿⣿⣿⣶⣦⣤⢆⡾⠑⢛⣏⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠠⠀⠀⠀⠉⠉
⠀⠀⠀⢉⠉⣝⣩⣽⠋⠁⢾⠉⠻⣭⣁⠘⠿⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣞⣛⡒
⠀⠀⠘⣩⣾⣿⡿⠁⠀⠀⠸⠄⠀⠨⡻⣷⣿⡆⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣐
⠀⠀⢸⣿⣿⡿⢁⠀⡴⣶⣷⡀⠀⠀⣩⣼⠟⠀⠦⠀⠀⡜⠁⠈⠛⡛⠙⠛⣿⢿⡿⠿⢿⡿⠿⠿⠷⡄⠰⡦⣶⣤⣶⡄
⠀⠀⠸⠿⢿⣥⠼⠿⠿⠿⠿⠿⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠋⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢡⠟⠛⠻⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⣿⣿⣶⣶⣿⣷⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⢋⣤⣾⡟⠛⡟⣿⣿⡿⠛⢿⣿⡟⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⡠⠚⣿⣟⣻⡟⠀⣿⣿⣄⠀⠀⠹⣇⡀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⣡⣶⠁⠈⠉⠏⠀⣿⣿⠛⠿⠀⠀⠸⣿⠇⠀⠀⠘⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠄⠀⠀⣠⡟⠁⣐⣆⠀⠀⠀⣿⠛⡆⠀⠀⠀⠀⠘⣷⣿⡀⠀⠀⢳⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠀⠀⣰⣿⠁⠀⠉⠉⠀⠀⠀⢻⣦⠀⠀⠀⣀⠀⠀⠻⠛⠟⠀⠀⠀⠘⢀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⢀⠛⡿⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠈⠀⠀⠀⢿⣤⠀⠀⠀⠀⠘⣦⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡅⠀⠀⠀⡘⢠⠇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⢇⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠘⢧⣿⠀⠀⢀⣄⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⣧⠀⠘⣄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠰⣷⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠙⡄⠀⠻⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠐⢁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⣸⣿⣿⣿⣿⣯⠉⠛⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠻
⠀⠀⠀⣿⡇⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⣵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆
⠀⠀⠀⣿⣟⣻⣿⣿⣷⣦⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠇
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⡀
⠀⠀⢸⣿⢸⣿⣿⣿⣿⠿⠃⠀⠄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⡇⢈⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣼⣧⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣿⣿⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣿⣿⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⣿⣿⢸⣿⣿⠉⡿⠁⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢹⣿⠸⣿⣯⢸⣦⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⢸⣿⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⡄⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⣿⡇⣿⣿⣿⢁⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⣿⣿⢹⣿⣿⣞⠛⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⢸⣷⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⣿⡉⣿⣿⣿⡧⡄⠀⠀⠀⢜⣿⠀⠀⠈⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⣿⣿⣆⡀⠀⠀⢸⣿⠄⠀⠀⠠⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⢀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⣠⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣼⣿⣥⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣻⡰⠶⣀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⣠⣾⡇⢀⣴⣨⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣴⣾⣧⣼⣤⣤⡼⣶⣿⣿⣳⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠟⠛⠿⠛⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠀⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⠖⠟⠳⢲⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢰⣶⣶⡆⢱⣶⣶⡆⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠾⢽⢯⠷⢀⢀⠆
⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡷⠀⠀⢸⣿⣿⡇⢸⣿⣿⠁⠀⠀⢾⣦⡀⠀⠀⠀⠈⠀⢰⣿⢾⣿⣄
⠀⠹⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⣸⣿⣧⣤⣄⠀⠀⠐⢿⠿⠀⠿⠿⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠸⠿⠿⠇⠸⠿⠿⠀⠀⠿⠟⠛⠉⠛⠛⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡁
⠀⠀⠀⠀⣸⣇⠀⠀⠀⠈⣚⣷⡴⠀⠀⢦⣴⣗⠚⠀⠋⣤⠀⠀⠀⠀⠀⢈⡉⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢀⡻⢟⡀⠀⠀⠈⠁⢖⣿⣶⣶⣾⣳⠋⠁⠀⠈⢃⡄⠀⠀⠀⠀⣈⡠⠄⠀⠸⠿⠆⠀⣀⠂⠀⡀⠀⠺⠿⠂
⠀⢻⣿⣸⣿⣿⣇⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣤⠄⠀⢀⣈⣁⡤⠖⠀⠀⠀⠀⠀⠈⠉⠹⣷
⠀⠈⠿⠋⠀⠀⠙⠻⠋⠀⠀⠈⣿⠛⠛⢻⠏⠀⢠⣦⠀⠀⢡⡆⠀⠈⣡⣀⡠⠵⠚⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⣾⣶⣶⣧⣄⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠀⠎⠸⠂⠀⠈⠈⠁⠀⠂⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣠⣶⣿⠓⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣾⣿⣿⠟⠃⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠐⠻⠿⠿⠀⠀⣤⣄⣻⣿⣿⣟⣠⣠⠀⠀⠀⢀⣴⣄⡘⠇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠂⠀⠀⠙⢿⣿⣷⣆⣹⡿⠋⠀⠀⣴⣿⣤⣬⣿⡆
⠀⠰⠿⠿⠿⠿⢿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠋⠈⠿⢿⠷⠀⠀⠿⠿⠀⠸⠿⠇
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⢀⣬⠁⠱⠆⠀⠀⠀⠀⠀⠀⠀⣔⣰⣶⣠⣾⣧⢀⣤⠀⠀⣴⡟⠛⠉⠉⠙⢳⣆⠀⠀⢀⣴⣾⣦⡀
⠀⠀⠘⢆⡛⣡⡿⡿⠳⠇⢀⠀⠠⠀⠀⢀⣹⣷⣽⣿⣿⣿⣿⠃⠀⢘⣿⠀⠀⠀⠀⠀⠀⣯⠀⢠⣿⡿⠟⢻⣿⡆
⠀⠘⠛⣤⠢⣤⠷⢆⠈⣘⠋⠀⢇⠀⠀⠸⢿⣿⣿⠿⠿⠟⠃⠀⠀⠀⢿⣤⣀⡀⢀⡀⣰⡟⠀⢺⣿⣭⢀⠰⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠘⠁⠙⠁⠀⠀⠑⠂⠤⠤⠤⠤⠤⠄⠂⠀⠀⠀⠀⠀⠉⠙⡿⡿⠛⠉⠀⠀⠈⠻⢿⣿⣿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠙⠛⠛⠛⠙⠛⠛⠛⠛⢳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⢀⠀⠀⣠⣀⠀⡀⠀⣀⡀⠀⠀⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⠀⢀⣠⣿⣷⡶⠟⠛⠂⠙⠛⠉⠉⠻⠿⠷⢠⡀⠈⣿⣆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢴⣿⡿⠟⠻⠁⠀⠀⠀⠀⠀⢀⣤⣀⣀⡴⠄⠀⣀⢙⣷⠿⠟⣃⡤⠓⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣠⣴⠿⠏⠀⠀⠀⡀⠀⣤⣤⣶⣶⣿⡿⠛⠿⠁⠒⠉⠉⠟⣿⣿⣾⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⠿⠁⠀⠀⠀⣀⣾⣿⣿⡿⠟⠻⠀⠀⠀⠀⠀⠀⠀⢀⠰⠟⠃⣿⢹⡏⢿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠷⡿⠾⠟⠉⠙⠀⠀⠀⠀⠀⠀⣰⣦⣤⣼⠿⠀⣀⣸⡗⢨⣇⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡄⣄⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠛⠀⠀⣨⣿⠋⣺⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣿⣿⠟⠛⠁⠀⢰⣶⣿⡿⢠⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢠⡀⠀⢠⣤⣿⣶⣿⣿⠋⠉⠀⠀⠀⢤⣤⣿⣿⣟⣭⣼⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣠⣿⣷⣿⠻⠛⠁⠀⠉⠀⠠⢰⣤⣾⣿⡿⡏⢛⠦⣼⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡛⠉⠙⠁⠀⠀⠀⣤⣄⣠⣷⣾⣿⠿⠛⣀⠈⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣤⣀⣴⣦⣴⣶⣿⣿⣿⣿⡉⠱⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣛⣻⡩⣁⣀⣼⢋⠘⣏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠙⠛⣘⡆⢹⡀⠀⠉⠀⣠⠀⡀⠃⡄⠀⠀⠀⠄⠀⠸⠠⠀⠘⢷⠀⠘⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢻⡀⢥⡀⠀⠘⠃⣴⠇⣴⠀⢠⡀⠀⣄⠘⣧⠈⢿⠆⠀⢰⠆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⡄⢹⣤⠁⠀⠀⠰⠏⠀⢸⡇⠸⣿⠀⠛⠀⠀⠀⣠⠎⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣀⠙⠲⠤⢀⣀⣠⣀⣀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⢤⣤⣍⣀⣠⠤⠔⠒⠁



⣿⠿⠿⠿⠿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠉⠳⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠘⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠎⠀⢘⠆⠀⢃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡄⠀⠸⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣿⡗⠀⠀⠀⠉⠙⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⢠⣤⣄⣿⣄⣠⡀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣾⣿⣿⣿⠄⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠸⣇⢹⣿⣦⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⣀⡿⠀⠻⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡀⣠⣴⢾⠉⠳⣶⣦⣤⣴⠖⠒⠂⠐⠒⠲⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢌⣷⠀⠈⣇⠀⢸⡟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠻⠆⠀⠀⠀⠀⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⢿⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡂⠀⣄⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠋⠀⠁⣸⣦⡴⠇⠀⠀⠀⠀⠀⠀⢀⣲⣶⣶⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠰⢠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣾⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡏⣀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣱⢃⣞⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⠋⠛⢹⠏⠉⠉⠉⠛⠁⠀⠈⠁⠛⠉⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠻⣿⠟⢻⠿⢿⠿⠻⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣶⣿⣶⣿⣷⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⢝⠛⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠐⠀⠣⣀⠸⢗⠠⠀⠀⠀⠙⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⠀⠀⠑⣌⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠳⣄
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢧
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡠⠖⠋⠱
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⡤⠖⠓⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠲⡉⠀⠈⢁⡰⠖⠃⢀⠄⠀⠀⠀⠀⠀⠀⠀⣸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠱⠂⠁⠀⠔⠊⠁⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠈⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠒⠂⠀⠉⠃⠋⠃⠀⠀⣈⣠⠔⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣡⠏
⠀⢹⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠈⣅⠂⡀⠈⠀⢀⢠⡐⠠⠠⠒⢁⣀⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡴⠃
⠀⠀⢳⡀⠀⠀⢸⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠑⠛⠢⠥⠴⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡥⠋
⠀⠀⠀⢳⡄⠀⠘⡌⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣂⠴⠋
⠀⠀⠀⠀⠙⣦⡀⢳⡀⠀⠀⠙⠻⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣠⠵⠊⠁
⠀⠀⠀⠀⠀⠈⠛⢮⣿⡄⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⣀⡀⠀⠀⠀⢉⣟⣷⣶⡶⠶⠶⠶⠦⠤⠶⠶⠶⠖⠒⠚⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢡⢠
⠀⠀⠘⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠆⠰⠈
⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠛⡘⠛⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠰⡇⠀⠀⠠⠤⠖⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠠⠄⠀⠀⠠⠠⠄⡄⠀⠀⠀⠀⡂⠆⠅⠀⠀⠀⠰⠰⠀⠀⠀⠀⡀⠀⠀⣠⢭⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠰⠠⠀⣃⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⡀⠀⠀⡀⢀⢀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢸⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⡀⢇⣃⠸⡤⡀⣧⣅⠈⣆⠀⠀⠀⠁⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⡀
⠀⠀⣩⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⢀⡄⡄⠀⣄⠀⢠⠀⡀⡀⢠⡀⠀⡄⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⢀⣿⡇⠀⠈⠫⣶⡽⠃
⠀⠀⡡⢖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠣⡀⠐⠇⠧⠀⠷⠄⠸⠀⠬⠄⠀⠧⠀⠧⠉⠆⠮⠐⠦⠰⠥⠀⠀⠠⠻⠛⠃⠀⠀⠀⣿
⠀⠀⠖⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠈⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢄⠐⠀⣠⠆⠀⠀⠀⡆⠀⡆⠀⢀⢀⠀⠀⠀⢀⣀⡀⠀⠀⣄⠀⠀⠀⢰⡿⠁⠀⢈⠀⠄⠀⠀⠁⢈⠄
⠀⠀⠀⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⣀⢠⠇⠀⠉⠑⠢⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠙⢣⡀⠀⠀⠘⢠⡁⠙⠢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠡⡈⠙⢤⡀⠀⠈⢃⠀⠁⢀⡉⠍⣙⣙⢒⠖⠒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠄⢁⠘⠑⠦⢤⠤⣈⡋⠉⠐⠁⠀⠀⠀⠀⠀⠀⠠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠑⠑⠂⠒⠊⠘⠁⠉⠒⠤⢀⠀⠀⠀⡠⠔⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡻⠔⠂⠁⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢅⡐⠠⠤⠤⣀⣠⠤⠤⠔⠊⣁⠴⠓⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠦⠔⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⡟⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣀⣀⢹⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣭⣭⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⡿⠛⠉⠁⢑⣽⢟⣿⡿⠟⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠀⠀⠀⠈⡴⠋⡠⢻⡟⠀⠀⠀⢼⡟⢸⣿⡆⠅⠀⠉⠻⣿⣿⢿⣿⣶⣵⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠐⢀⠞⠀⠈⡴⣿⠀⠀⠀⠀⣿⠱⠈⢻⡇⠀⠀⠀⠀⠘⢿⡣⣉⠙⠛⠻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣠⠞⠋⠀⠀⠀⠀⢀⠴⠁⠀⢀⡼⢡⡏⠀⠀⠀⠀⡿⣇⢀⢣⠵⡀⠀⠀⠀⠀⠩⢧⠈⢣⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⠀⠀⠀⠀⣠⠎⠁⠀⠀⣰⢟⣴⠟⠀⠀⠀⠀⠀⢹⣿⡈⣾⡆⠳⠀⠀⠀⠀⠀⠻⣄⠀⢣⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⠀⠀⢀⡾⢣⠖⠈⢹⡞⢡⠞⠁⠀⠀⠀⠀⠀⠀⠈⣿⡇⢹⡇⠀⣇⠀⠀⠀⠀⠀⠙⣷⣄⢷⡀⣀⣼⣯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢀⡞⡱⠁⠀⠀⡈⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⡇⠀⠸⠂⠀⠀⠀⠀⠀⠘⢿⣗⡍⠙⠉⠋⢻⣅
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣾⣾⠃⠀⢀⠃⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣥⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠻⣾⡂⢄⠀⠀⢿⡄
⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⣸⣿⡏⣆⣠⠊⣰⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣿⠋⣠⣃⣰⡄⠀⠀⠀⠀⣀⣵⡌⢷⡀⡇⢀⢸⣇
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣠⢯⣿⢏⠈⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⢹⠏⠉⠉⣉⣿⣦⣶⠂⠀⠁⠀⢿⠈⣷⣿⢘⣾⣿
⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⢠⣯⣞⠵⢠⡄⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⠞⠂⣚⣙⠀⠀⠉⢹⡇⠀⠀⠀⢸⣶⣿⠏⡟⠙⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠛⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠉⠀⠀⠀⠠⠾⠿⠛⠂⠀⠀⣁⡁⠀⠀⠀⠸⣿⡏⣷⠃⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠐⠀⣿⡆⠀⠀⠀⠀⠈⢁⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⢀⠀⠘⠃⠭⠿⠀⠀⠀⠀⣿⢑⡟⠀⠀⡟
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠀⣿⠃⠀⠀⠀⠀⠀⠛⠋⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠸⢍⠉⠁⠈⢀⡄⠀⢉⡉⠀⠀⠀⢰⡟⣸⠇⠀⢰⡇
⠀⠀⠀⠀⠀⢻⡇⡀⢀⢠⣀⣿⠶⠒⠂⠀⠐⠙⠀⢀⠜⢁⠀⠀⠀⠀⣴⡆⠸⠀⠀⡀⣿⣿⡄⡄⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⣸⣧⡟⠀⣠⡿
⠀⠀⠀⠀⠀⣨⠿⠛⢿⣯⠵⠚⢀⠁⢀⡀⠀⠀⠐⠛⣠⣿⡇⢀⡖⢼⣿⣿⢰⠀⠉⠐⠈⠉⠀⠃⠀⠀⠊⠀⠀⢀⡏⠀⠀⠀⠀⣿⡟⢇⣴⣿⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠈⠶⠛⠀⠀⠀⠛⠡⡂⠀⠀⠀⠈⠛⠁⠛⠀⠈⠉⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⢸⣿⢻⣴⣯⡟
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣏⣸⣿⡟
⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠏⡷⣸⣾⡟
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⢏⡾⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠤⣄⠂⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡵⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⠄⠐⠒⠒⠛⠛⠉⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠁⠂⠤⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠈⠉⠑⠢⢄⠋
⠀⠈⠀⠀⢀⣶⣶⣦⣤⣀⡀⠀⠀⠀⠈⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠁⠀⠀⠀⠙⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠈
⠀⠀⠀⠀⠸⣛⣿⣶⣾⣤⣿⡶⢄⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢘⠀⠀⢀⣤⠆⣖⣶⡦⣤⣤⣀
⠀⠀⢀⠀⠀⠈⠚⢿⣿⣷⣿⣟⡃⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣌⣀⡀⠀⠀⠀⠀⠀⠐⠁⡎⠀⠀⠠⣾⠹⣭⣽⣛⣹⢿⣿⣧⡟⣢⡀⠀⠀⠃
⠀⠀⠀⠣⡀⠀⠀⠀⠈⠙⠛⠫⠽⠒⠀⠀⠔⠀⠀⠀⠀⠄⠀⠀⠀⠉⠘⠋⡃⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠃⢫⣯⣿⡋⠟⣋⣽⣿⣿⠂⠀⠀⢀
⠀⢰⠁⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣠⠊
⠀⠀⠀⠀⣀⣄⡈⠑⠂⠤⢀⣀⣠⠴⠊⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⢀⣾⣿⢿⡷⢦⠀⠀⠀⠀⠀⢄⠀⠀⠈⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠒
⠀⠀⢲⠆⠈⠿⢿⣆⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠸⠉⠿⣀⣠⣴⣿⢤⣤⡄⠀⠀⠁⠠⠀⠀⠀⠀⠈⠉⠀⢉⣈⡉⠉
⠀⠀⢘⣆⡀⢀⣼⡫⢤⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠊⣀⣾⡗⠺⠏⣩⣴⡛⠀⠁⡀⠀⠀⠢⠀⠀⠘⠀⠀⢀⠖⠋⠁⠹⣶⣦⣠⡤⢴⠇
⠀⣰⠟⠛⠉⡇⣾⡇⢰⡿⠓⠂⠀⣤⣯⡀⡀⠀⠀⠀⠀⠀⠀⢤⢰⣿⣷⠄⠀⠀⣹⣵⡀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⡀⣿⡟⠁⠀⠀⠀⣴⡄
⠀⠻⡀⠀⠀⣹⠟⠉⠉⠀⠀⠀⠈⠏⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⡃⢀⣀⡰⠟⠻⠟⠦⠔⠃⠀⠀⠀⠀⡦⠐⡄⠀⠀⢼⣤⠶⢾⣛⢣⡀⠀⣘⣿⣿⠇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠠⣀⡀⠀⠀⡰⠀⣈⠀⠀⠑⠀⠀⠀⠈⢻⠿⠻⠓⠝⠶⠟⠛⢁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⢸⣄⢀⡀⠀⠀⠠⠄⠀⠠⠐⠁⠀⠀⠀⠉⠳⣌⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠰⣶⣴⣄⣞⣠
⠀⠀⠀⠓⠄⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⣠⣠⣤⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠿⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠢⣀⡠⠂⠌⠀⠀⠀⠰⣬⡿⣿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠂⠑⣆⠀⠀⡌⠀⠀⠀⠀⣽⣿⢶⡈⢷⠀⠀⠀⢸⠀⠀⠀⡦⠀⠀⠀⠀⠒⠷⣶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣄⢤⣮⢷⡀⠀⢀⣼⠀⢰⠁⠀⠀⠀⢨⣿⣿⢸⣦⡽⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠟⠉
⠀⠀⠀⠀⠀⠂⠀⠄⠬⣼⡿⠀⠠⢤⣿⠦⠐⣿⡈⠟⠺⣿⠃⠀⢸⠀⠀⠀⠀⠸⢿⣿⣿⣗⡗⠀⠀⠀⢰⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠁⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠛⠀⠀⠀⠸⣿⠝⠪⣾⡁⢀⠀⢈⣆⠀⠘⡄⠀⠀⠀⠀⢇⡽⣮⡵⠀⠀⠀⠀⡘⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠘⣿⣿⣤⠜⣀⠄⠀⠳⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⢀⡜⠀⠈⠀⠈⠆⠀⠠⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠈⠒⠤⢄⡤⠤⣄⣀⠠⠐

⠀⠀⣤⣤⣀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⣀⡠⠀⢤⣤⣤
⠀⠀⢹⣿⠋⠀⠹⣿⡏⠀⠹⣿⡯⠉⢽⣿⡷⠀⠲⣿⡶⠂⠰⣾⡶⠂⠰⣟⡶⠃⠈⢻⡿⠏⠈⢻⡿⠇⠀⠛⣿⠇⠀⠐⢿⠏
⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠈⠛⠀⠀⠀⠻⠃⠀⠀⠸⠃⠀⠀⠸⠇⠀⠀⠈⠏⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⡴⠄
⠀⠀⠀⠀⢛⣼⡺⠀⠀⠀⠀⠀⣻⣿⣿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⢠⣆⣀⠀⢿⣿⡘
⠀⠀⠀⠀⠀⠉⠁⠐⣶⣾⣇⠀⠈⠀⠉⠀⣾⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⡃⠈⠁⠈⠁⠀⠀⣀⠀⠘⢻⣿⣿
⠀⠀⠰⠖⠀⠀⠀⠰⠿⢿⡏⠁⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⣷⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⡞⡹⠇⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠘⠿⠾⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠁⠁
⠀⠀⠀⢀⡾⠿⠞⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠖⠄⠉⠃
⠀⠀⠀⣿⣧⠀⠀⢈⣿⡇⠀⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⣀⡀⢘⢋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡀⢀⡀⣀
⠀⠀⠀⠻⣿⠀⠔⢺⡿⠃⠀⠨⢛⣧⣧⠀⠀⡟⠶⢻⠀⡧⠄⢸⢴⠃⣯⢼⠁⢱⠎⠀⠀⠈⠁⠁⠀⠀⢛⠋⣉⣡⣟⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠈⢀⠃⠃⠈⠀⡁⠁⠈⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠊⠀⠀⠀⠀⠙⠁⠘⠃⠑⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠈⣠⣤⡀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣂⠀⠈
⠀⠀⠀⠰⣾⣷⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡄⠀⠀⠐⠽⠿⠯⠛⠄
⠀⠀⠀⢀⣝⣛⡿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⡖⠀⠀⠠⣄⣀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠹⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠠⡾⠃⠀⠀⠀⡞⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠤⠄⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠿⠿⠶⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣀⡀⢮⣷⡄⠀⠀⠀⠀⢀⡴⣆⣠⣄⣤⣀⡄⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢮⠅⠘⠛⠀⠀⠀⠈⠀⠠⢤⣀⠀⢠⣀⣈⡀⠀⠁⠠⠄⢀⣠⡼⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⠀⠀⠁
⠀⠐⠀⠀⠄⠤⠀⠀⠀⢀⣠⡝⠁⡈⣿⠇⠀⠀⠀⠀⠀⠀⢠⣦⣴⣦⣴⣦⣤⠀⠀⠀⠀⢿⡏⠋⠁⠀⠀⠀⠀⠒⠒⠲⠆⠐
⠀⠀⠀⠀⡀⠀⠙⠿⠛⠛⣿⣇⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠒⠒⠘⠋⠙⠀⠀⠀⠀⠀⠐⠋⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢘⣧⢀⡤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠟⠋⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⠀⢸⣷⣋⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡋⠀⠀⣠⠞⠫⠧⠵⢭⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣠⣾⠋⠀⠀⠀⠀⣀⣤⡶⠶⠶⣤⣀⠀⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠔⣁⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢒⣚⣻⡿⠁⠀⠀⢀⡴⢾⢣⡶⠔⠛⠈⠁⠀⠀⠀⠀⢠⣥⠀⠀⠀⠀⠀⠀⠀⣠⣾⠯⠚⠉⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⡋⠁⢤⡿⠁⠀⠀⡀⠼⠟⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢠⡟⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⠀⣊⣿⠃⣀⡔⠚⠃⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡏⠈⢢
⠀⠀⠀⠀⠀⠰⠆⣿⡿⠚⢦⠛⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠘⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢉⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠰⣞⣁⠀⠶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠰⠈⢳⢤⣀⠀⢀⠀⢠⣴⣬⣹⣞⡻⣿⠿⠃⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠙⢭⣳⣴⣄⣠⣄⡄⠀⠀⢠⡄⣦⠘⠴⡈⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠻⣯⡀⠀⠀⠀⠈⠉⠘⠛⢿⣾⡴⠒⠘⠚⠂⠛⠉⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⣂⣀⣉⣓⡛⡌⠉⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠢⠀⠉⠿⢷⣶⣤⣤⣤⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠀⣤⢀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠏⡼⢰⠇⣼⠃⡴⢣⠶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⢄⠀⠀⠘⠀⠈⠸⡅⠘⠀⠣⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⢀⣀⣤⣄⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀⡠⠚⠙⠤⡴⣟⣦⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢠⠔⡿⣼⣾⣷⣶⣰⡿⢿⡇⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠴⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⡛⢤⣠⣇⣿⢇⣼⡽⢳⣾⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⣤⠀⢀⠉⠀⠰⡦⠂⠀⠄⢉⡙⠙⠚
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠇⣻⣿⡽⠇⢩⡿⣷⣿⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠢⡀⠀⠈⠀⠇⠎⡀⡀⠔⠊⠨⠤⢼⠁
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠉⠛⠻⣿⡿⠇⠞⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠒⠲⡂⢰⢌⠃⢘⠀⠠⢀⡤⠐⠋⠠⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠹⣿⣦⣄⡀⢀⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠈⠃⣈⠙⠢⣇⠈⣦⠴⠋⢠⣤⠤⠶⠂⡀⠐
⠀⠀⠀⠀⠀⠀⠙⠛⠩⡋⠉⢹⠙⣦⣀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣶⡏⢩⡐⠠⣀⣀⡀⠠⠜⠓⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⣄⢛⣳⣶⡦⣤⡴⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⣧⣄⣤⡙⡉⠒⠶⠈⣀⢠⣀⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠘⠆⠁⢤⡁⠉⠚⠦⠤⠦⠀⠀⢤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠚⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠉⡿⠋⡟⠉⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠌⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡕⠄
⠀⠀⠀⠀⠀⡀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⡀
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡀⣗⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿⠠
⠀⠀⠀⠀⣹⣧⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⡸
⠀⠀⠀⠀⠰⣷⣀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣧⠁
⠀⠀⠀⠀⠀⢿⣧⠀⠀⢿⣆⠀⠀⠀⠀⢠⠀⠀⠀⣼⡇⠀⡀⣾⡇
⠀⠀⠀⠀⠀⠀⢿⣾⣾⠘⣿⣆⠀⠀⠀⢈⠀⠀⢀⣿⢑⡧⣴⠏⠀⠀⢀⡀⠤⠄⠀⠤⠄⠀⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣽⣿⣶⡄⣰⢺⡆⢠⣼⣷⣾⡿⢁⠠⠒⠊⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⡿⣿⣿⣷⡿⠿⠟⠉⠐⠁⠀⠀⠀⢴⣒⣦⣄⣀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⡾⣟⡞⣛⡷⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⢤⣚⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡂⠐⠀⠀⠀⠀⠀⠀⠉⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣠⣠⣦⣤⠴⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡠⣫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⡴⡫⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⠀⣰⢶⡫⣮⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⢀⣄⣴⣿⠵⣫⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣿⣿⣿⡿⠛⠃⠈
⠀⡀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣚⣿⣻⡿⠁⠈⠁⠈⠀⠀⠀⠀⠀⠂
⠠⣭⣑⠪⢭⣛⣓⠶⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣲⡦⣶⣻⣿⡿⢹⠂⣤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠉⠓⠲⠯⣭⣛⣒⠦⠤⣄⣀⣃⣀⠀⠀⠤⠤⠄⠒⠛⢽⣿⣷⣶⠟⣽⣻⣯⣿⠻⢶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⢤⢭⣽⡿⠏⢠⣤⣾⡖⢋⣽⠗⣂⡀⢸⣧⣿⠟⠓⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣤⣌⣛⣺⣿⣿⣭⣾⠟⠁⠀⠀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠤⠄⠀⣀⠀⠀⠀⠈⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠠⡀⠀⠀⠀⠁⠀⠀⠀⢻⡷
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠂⠁⠰⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠐⠒⠊⠉⠀⠈⠐⠀⢀⠀⠀⠀⠀⠀⠀⢠⢨⡗⠀⠀⠀⠀⠀⠤⠥⠄⡀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⡴⠞⠉⢁⠀⠄
⠀⠀⢀⡴⠋⠀⠀⠀⠈⠓⠈⠄⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠂⠀⢠⠀⠀⠀⢀⡴⠒⢒⠒⠒
⠀⢠⠟⠀⠠⣄⠀⠙⠀⠀⠀⠈⢆⢇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠊⠁⠀⠀⠈⠀⢸
⠀⡟⠀⣄⠀⠀⠀⠀⠦⠀⠀⡀⠈⢞⡆⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠀⠀⠀⠰⠄⠀⠀⡞
⠸⡇⠀⠈⢀⡀⠀⠀⠀⣄⠀⠉⠀⠈⢟⢆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠉⠁⠒⠒⠂⠤⠤⢀⣀⣀⠀⠀⠀⠈⢎⠳⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⣦⠀⠀⠀⠠⡄⠀⠲⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠆⠘⠂⠈⠳⣄⡀⠀⠀⠈⠀⡆⠀⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠒⠦⢤⣀⣀⣀⣀⣀⣀⡤⠴⠚⢁⡠⠂
⠀⠀⠀⠀⠀⠀⢀⣤⡴⢒⡴⢚⠿⡗⡶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⡂
⠀⠀⠀⠀⡠⣪⠟⣡⣴⠋⢰⣏⠀⣹⠈⣧⠙⣎⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢢⠠⠀⠀⠞⠊⠡
⠀⠀⢀⢊⣴⠋⢰⡿⠃⢠⣾⠟⠀⣿⢆⣿⠀⣿⡄⢹⣦⠀⠀⠀⠀⠀⠀⡀⡀⠀⠡⡀⠁
⠀⢀⢾⣿⠃⠐⣿⠁⢀⣴⡿⠀⣼⡿⢸⡇⠀⢻⣷⠨⣿⣧⠀⠀⠀⠀⠀⠄⠈⠙⣄⢁⠀⠀⠀⢀⠐⠂⠄
⠀⠸⢸⡇⠀⣾⣿⠀⣼⣿⡆⠘⣿⡇⢘⣿⠄⠘⣿⡇⢻⡿⡀⠀⠠⠊⠈⠚⢄⠀⠀⠉⠀⠀⠂⠀⢀⣀⠈
⠀⢠⣾⡄⣼⣿⠋⢀⣿⣿⠀⣴⣿⠃⠸⣿⡆⢀⣿⠇⢸⣧⠃⠀⢈⠤⠀⠒⠣⡓⢄⠀⡄⢀⢀⣀⣉⣠
⠀⠘⣼⣇⢸⣿⡆⢺⣿⡅⠀⣸⣿⣷⠀⣿⡇⠈⣿⡧⢸⡿⠀⠀⠈⠒⠠⢄⠀⠱⡼⠰⡐⡡⠊⠉⠀⣀⠇
⠀⠀⠡⣿⠘⣿⡁⠸⣿⠁⠀⢹⣿⠃⢀⣿⡇⠀⣿⡇⣸⠃⠀⠀⠀⠔⠂⠉⠁⠀⢀⠃⠁⠀⡠⠤⠄⠐
⠀⠀⠀⠙⢦⠈⢿⡀⢹⡄⠀⢸⣿⠀⢀⣿⠏⣴⢟⡴⠁⠀⠀⠀⠈⠄⠀⠀⠀⠀⡝⠑⢄⡀⠀⠉⠳
⠀⠀⠀⠀⠀⠑⠤⣙⣄⡙⢦⣼⣏⣤⡾⢃⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠒⠠⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣚⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢀⡀⠀⠀⠀⠀⣀⣾⣥⡠⡀⠄⠠⣀⣠⠒⠀⠐⠒⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠌⠉⠉⠓⢀⢸⣧⡄⠀⣰⠟⣁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣿⣥⣾⣧⠞⠛⠋⠐⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠔⠭⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠀⠀⠈⠉⠒⠄
⠀⠀⠀⠀⠀⢀⠀⢠⠔⢣⠖⠀⠀⣠⠋⠀⠜⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠑⡀⠀⠄
⠀⠀⠀⠀⠀⢁⠐⡙⠋⠓⠀⣠⡪⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠷⡀⠀⡄
⠀⠀⠀⠀⢀⣏⠄⠀⠀⠀⣴⠉⢀⠀⠀⡴⠀⠀⠞⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢱⠀⠙⡀
⠀⠀⠀⠀⢸⣩⠀⠀⠀⡜⠁⠀⠬⠀⠰⠀⠀⠀⠌⠀⡜⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⣾⢻⠀⠀⢰⠃⠀⠂⠊⠀⠀⠀⠀⠀⠀⢠⠇⠐⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠂⠀⠀⠈⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣴⡄⡄
⠀⠀⠀⣵⠏⣫⡄⠀⡟⠶⢃⢰⡧⠀⠀⠀⠀⠂⠀⡬⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⡀⠀⠀⠀⠰⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⡸⡄⢀⠄⠀⠈⠿⠿⡃
⠀⠀⠀⣿⣸⣿⣼⣾⡇⣸⠃⣼⠀⠄⠀⠀⢠⠀⢰⡇⠀⢠⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠁⠀⠈⡀⠀⡀⢀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠳⡀⠀⠀⠈⢠⣼⡇
⠀⠀⠀⢹⣿⡿⢿⣿⡇⢿⣦⢿⣷⣀⠰⠀⠈⠀⢺⡇⡇⠘⡄⠀⠀⠀⠀⠀⡆⠀⢰⡄⠀⠀⠀⢸⣶⡄⠇⡘⠄⠀⡀⠀⠀⠑⠀⠐⠀⢀⡇⠐⠀⠀⢺⢧⡇
⠀⠀⠀⢸⡇⡅⣻⣾⠁⡈⠹⢚⣄⠀⢠⢀⠀⠀⣿⡇⠁⠀⠙⡆⠀⡀⠀⠀⡝⠀⠐⠂⠠⠀⠀⠀⢩⣷⡆⠀⢀⠀⠀⠀⠆⠀⠉⠁⠀⢘⠃⠀⠀⠀⠸⠸
⠀⠀⠀⢸⡙⣿⢸⡿⡇⢿⡇⢰⠀⡄⠀⠈⠃⠀⣘⣧⡀⢀⡆⠀⠈⡄⠰⢠⡄⠛⢀⠀⣤⠀⠀⠀⠀⢹⡇⠀⠀⠁⠈⠀⢀⠀⠀⠀⠀⢸⡆⠀⠰⠂⠁
⠀⠀⠀⠀⣿⣏⣾⣇⣧⢸⡁⣆⡆⠛⢀⠂⢦⣀⣿⣏⢷⡸⣿⡄⠀⢳⠀⠬⠍⠓⣶⣦⡌⠉⣤⠀⠀⢸⣧⡀⢸⡀⠀⠀⠸⠀⠀⠀⠀⣼⢁⠀⡁⢠⡖
⠀⠀⠀⠀⠘⡟⠟⢯⣇⣯⡻⢷⣗⣴⣨⠛⢳⣞⣿⡧⢸⣧⡀⣎⠀⠸⢸⣄⣀⠀⢠⣉⠆⠀⠉⠀⠀⣿⣯⢛⡈⠷⢠⠀⠀⠀⢰⠁⣠⠏⢎⡞⣧⠃⠃
⠀⠀⠀⠀⠀⠘⢦⡳⢼⣿⢿⡰⢹⣿⡜⣷⢿⣴⣿⣿⠺⢿⣛⣾⣧⣅⠀⣈⢉⡀⠈⠹⣦⡀⢦⣠⠀⣿⣏⠊⢷⢂⡌⢁⣶⢠⠆⠀⢠⣠⢼⡃⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠿⢤⣮⣿⣤⡠⡟⢭⣮⣼⣽⣿⡄⠰⣇⡼⣇⠺⣾⡥⢨⣛⣆⣀⣩⣥⡀⠄⣺⣿⣟⣡⠴⢋⡁⠀⣤⢛⡴⢰⠟⠓⠏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠮⣷⣾⣯⣭⢻⣌⠙⠺⣞⠲⠶⣶⣌⢉⡿⢥⡤⣷⣴⢽⣿⡗⡭⣰⣾⣽⠟⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠘⠟⠾⣶⣬⣿⣿⠻⣿⣳⢠⠤⡘⢛⠹⠿⣯⣭⡥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠐⠂⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠢⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⠀⠀⠑⠀⢤⠀⠈⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⢤⠐⡀⠀⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠈⠙⠀⠀⠀⠒⠈
⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⣆⠰⣄⠩⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠇⠀⠈⡀⠀⠀⠀⠀⠀⠀⠸⣦⢓⠀⢱⠀⠀⠀⠀⡆⠀⠀⠀⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡃⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⢀⠀⠀⠀⠀⠀⠀⠄⢒⠃⠀⠀⠀⠀⠨
⠀⠀⠀⠀⢀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⢐⢀⠐⠀⠠
⠀⠀⠀⠀⠀⠢⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠈⠀⠀⠠⡤⠄⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠐⠢⣔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢔⠠⠃⠼⠭⠝⠒⠰⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠴⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⡠⠋⠔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠻⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢀⠄⠀⢀⠤⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢰⠃⠁⠀⠀⠀⠀⠐⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠓⢃⠀⠀⠐⠀⠀⠀⠀⠰⢰⡀⠀⠡⢠⠀⠀⠂⠀⠀⠀⠀⠀⡅⡃
⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠐⠲⠀⢠⠁⠀⠀⠀⢸⠂⠀⠄⠈⢃⠀⠀⡀⠁⠀⠀⠀⠀⢀⠻⢛
⠀⠀⢸⠁⠀⠀⠀⠀⡦⡄⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠍⢸⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠎⠃⣈⠀⠀⠀⠀⠀⠀⡌⠀⢸
⠀⠀⠠⠄⠀⠀⠀⢠⡖⠀⠀⠀⠀⠁⡀⡟⠀⠀⠀⠀⡼⢀⠆⠀⠀⠀⠀⠀⠀⠀⠉⠐⠦⡤⠀⠚⠉⠀⠀⠀⠀⢀⢘⠀⠀⡺
⠀⠀⠀⢅⠀⠀⠀⠘⢯⠀⠀⠀⡀⠔⠛⠀⠀⠀⠀⡔⢀⡎⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⣰⠃
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠠⠀⠊⠁⠀⠀⠀⠀⠀⡂⢠⠎⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁⢖⡠⠄⢤⠄⠴⡒⠮⠁⡁⠀⠀⢀⠦⠋
⠀⠀⠀⠀⠀⠀⠉⠠⠤⢤⠀⣤⣤⡥⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⢨⢤⣄⡤⠠⠔⠐⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡟⣻⢿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣂
⠀⠀⠀⠁⠐⠒⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⢀⡾⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⢀⠀⠀⢀⠾⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢄
⠀⠀⠀⠀⠀⠀⣠⡐⠋⣀⡼⠁⠀⠀⣸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠈⠙⢿⢤⣄⡀
⠀⠀⠀⠀⢠⡥⠋⢠⡿⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠉⠉⠋
⠀⠀⠀⠀⠛⠓⠋⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠈⠐⠂⠠⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠘⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⣂⠀⡤⠤⣀⣒⠴⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣭⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠉⢱⣿⣿⣿⡿⣄⣴⣶⡖⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⠾⣿⢻⣟⢛⣿⣾⠟⢻⣷⣟⣩⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡀⣀⠑⠾⣍⠈⣶⣾⣿⣾⣿⡟⣵⣢⣶⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣢⡅⠐⣿⣣⣤⠞⣟⠷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣥⣾⣖⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⠀⠀⠘⣿⠁⢸⣿⡤⡴⡆⠈⡇⣿⣿⣿⣿⡿⣿⣶⢮⠙⠡⠷⠈
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣧⣿⡟⣀⣠⣯⣾⠿⣿⣿⣿⣿⣧⡜⠋⡀⣰⠆⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠐⢻⡿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠟⠁⠸⡦⠚⣋⢤⣿⢿⣿⣿⣿⣿⣟⡿⢛⣿⣿⣿⡛⣟⠒
⠀⠀⠀⢀⠀⠀⠀⠠⠇⢙⢿⣿⣿⣿⣿⡿⠋⢀⣰⠓⣲⢶⣶⣇⣈⢀⣾⣿⣿⣿⣯⡾⢛⡋⢒⡀⠀⠈⠛⠁
⠀⣤⣶⣿⣿⣆⡀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠴⠛⡷⣤⣌⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠁
⠀⢿⣿⣿⣿⣿⣷⠻⣧⠀⣤⡜⣿⣿⣿⣿⡤⢬⡛⠻⠟⣿⡟⣿⣿⣿⣿⣿⣿⣿⠉⡜⠉⢩⠓⠂⣠⣤⣤⣀⠀⢀⣀
⠀⠈⠻⢿⣿⣿⣷⣄⣿⣾⡏⣰⣿⣿⣿⣿⣗⠛⢨⡿⠷⣬⣥⣤⣿⣿⣿⣿⣿⣿⣶⣿⡶⣾⡂⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡇⡋⢀⣻⣿⣟⣻⣿⣿⡿⠛⣻⠿⠻⣿⣿⣯⡥⡀⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⠀⢿⣿⣿⣿⣿⣿⡾⠋⣟⣼⣟⣻⣿⣿⡇⠀⣿⠀⢀⣿⣿⣿⣫⠥⢈⠀⠀⡉⣉⣀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⣿⣷⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡶⠢⠁⢠⠚⠙⠛⢛⣿⣿⠁⠀⢨⣿⣿⣿⣿⣏
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣘⡇⠀⠠⠐⠴⠿⠾⠛⠛⠁⠀⠀⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢻⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡿⣷⢾⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣷⣤⡀⣷⣶⣂⣠⣾⣧⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢘⣿⡿⣿⣿⠁⠠⢼⣧⣿⣿⢟⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⡽⠿⠻⡅⣟⢀⠀⢸⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢰⣿⡏⣿⡟⠀⢸⣿⠁⠸⣿⣰⡶⠛⠙⠁⠀⣮⠀⠀⢸⠟⠇⠸⣀⠟⠛⢿⣛⣿⠀⠀⢰⡇⠁⠀⡇⢸⠀⠀⢸⣿⣇⢸⣿⣷
⠀⠀⠀⠀⠈⣿⣹⣿⠇⠀⢾⣿⡀⢴⣿⣏⠁⠀⠀⠀⠀⣿⠰⠄⣻⠶⠀⠄⣿⠀⠀⠀⠿⠀⠀⠀⢸⡇⠀⠀⡇⠈⠀⠀⠸⣿⡟⠸⠿⣿⠇
⠀⠀⠀⠀⠈⠛⠻⣿⣷⣄⠈⢿⠄⠀⠸⠿⠀⠀⠀⠀⠀⠿⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⠿⠃⢤⣾⡿⠇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⣤⠤⣤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢦⡴⣟⠢⣶⣤⣌⣤⠞⣠⣄⡰⢦⢀⠀⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣶⣿⠦⢤⡄⣀⣀⢅⣀⣰⣸⡀⡄
⠐⣻⡅⠋⠑⠿⡟⢫⠈⢨⢈⣟⢫⠉⣿⠓⣹⣩⢇⡀⡀⠀⣤⠀⠀⣀⣀⡼⢀⠮⠂⢪⡇⣿⣣⡉⣿⡿⢁⠺⡘⣯⠼⡦⢿
⠈⢇⢓⡦⡟⡾⢹⡼⢗⣙⢈⡷⣈⡻⠖⢢⠒⣶⡐⣿⡟⣿⡙⢿⣿⢽⡿⣺⣍⣌⣇⣰⣆⠺⠧⡑⠾⣷⠈⠠⡌⢓⢂⡟⡶
⠀⠀⠼⡆⢉⠗⢜⠓⠎⠴⢖⣄⡹⠟⢵⣡⠟⡀⢌⡙⢶⠉⣐⠈⠷⠠⠃⠄⡂⣹⣧⢧⢸⠌⣣⡘⢲⢦⠈⠇⢉⠘⠾⠑⢹
⠀⠀⢠⠀⡌⠁⠄⡐⠀⠀⠈⠀⠁⠚⠂⠛⠀⠸⠾⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⢄⠉⠠⡌⠳⠶⠌⠀⠁⠈⠈⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁⠀⠑⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⠱⢦⡠⣤⣄⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣿⣥⡀⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⢞⡛⠟⠛⠛⢛⡛⠿⠿⡿⣧⣭⠃⠐⠆⠓⠂⠶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡷⠞⡝⠛⠁⠲⡀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠆⡀⠄⠀⠉⠋⢁⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⠟⣹⠍⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣿⠛⣇⠖⢁⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣼⡿⣿⣵⡞⡿⢾⣬⡅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢰⡿⢿⠽⣾⣫⣿⡯⢟⠿⡟⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤
⠀⠀⠀⠀⠀⣠⣿⠳⣎⣢⠛⣾⣿⣲⣽⡻⢳⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢐⣿⣿⠀⣦⣥⣶⣬⣷⣽⣶⣓⡌⢡⡍⠖⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄
⠀⠀⠀⠀⣼⣛⣾⣥⢶⣿⢯⡳⣿⣉⣿⡅⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠐⢧
⠀⠀⠀⢠⣾⣿⣿⣿⡿⢿⣾⣿⣷⣻⣿⣿⡏⠈⠀⠀⠀⠐⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣼⣯⣩⣽⣯⣏⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣟⣿⣽⣧⣟⡷⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣷⣔⡋⢘⡈⠂⠀⠀⠀⠀⢂⡁⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⢻⡃
⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠗⠀⢡⡀⠀⢀⡀⠀⠀⠁⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⣽
⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠶⠛⠄⠀⠈⠠⢀⡞⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⣁⡟
⠀⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⢺⡟⠛⠶⠀⠀⠄⠃⠰⠇⡀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⡿⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡧⣤⣰⡶⠗⢈⣬⣱⠂⢁⡤⡃⠐⠡⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⢠⢀⠂⡄⢀⡸⣛⣈⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣼⣛⡿⣋⡝⣴⡁⡄⠀⠈⠀⠀⢠⡠⡆⡈⠁⠀⠀⠀⠀⠀⢐⠀⢆⠘⠢⡘⣷⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇⣸⡝⠷⠤⠄⣡⣢⠘⠔⣁⢀⡈⠀⢈⣉⢩⡄⣃⣨⣴⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣟⣿⣷⣤⢼⣷⡿⣟⡾⢾⣿⡜⣄⣻⡆⣳⣀⣠⣿⣶⣟⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢼⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋

⣿⣿⡿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠀⢀⡀⠀⠀⠁⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠒⠙⣤⣀⣙⢠⣆⡥⠀⡀⠂⠀⠨⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠈⢹⣏⣰⠞⠳⠚⢉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⣀⣀⣘⣿⠀⠀⠀⠀⠉⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⠀⠲⢤⠀⣄⠐⢋⡟⠁⠀⠀⠀⠛⠀⠀⠀⠙⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠈⢧⠀⠀⠀⣤⣈⡀⠀⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢂⣤⠀⠀⠀⢀⣴⣾⣹⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⡝⠛⢿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠰⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⢈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠈⠢⠔⠀⠀⠀⡂⠀⠈⠀⠀⠀⢠⠀⢀⠀⢀⣠⠆⠁⠀⠀⠼⣏⠀⣺⠃
⠀⠀⠀⠀⠀⠀⠲⠘⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⠀⠀⠀⢸⣇⠀⣠⣸⠃⠀⡀⠀⠀⢠⣧⣼⣻
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠚⢣⠤⣄⡀⠀⠀⠸⡇⠈⠀⠀⠀⠀⠠⠈⠑⣿⣷⡃⣸⣇⠤⠐⠁⠀⠈⠻
⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠐⠀⠉⠀⠀⠀⠈⠳⠶⡀⣁⠀⢁⠒⢦⡀⠀⠀⣈⠙⡿⠛⣿⣏⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠿⢇⠀⠓⠀⠁⠀⢹⡇⠀⠀⠐⠈⠁⠆⠠⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢣⢀⡐⠢⣀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠱⢴⣆⠁⠐⢻⣿⣄⠀⠀⠀⠀⠁⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⣈⠁⠀⠛⠀⠃⠘⡰⠋⠉⠈⠁⠐⠂⣹⣆⠀⠹⣿⣿⡧⠐⠁⠀⠀⡞⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⡐⠒⠁⠀⠀⢀⡀⠄⡴⠂⠈⠛⠄⠈⣿⣠⡶⣄⣀⠀⢨⠷⢲⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⡐⠀⠀⠀⠀⢌⡤⢹⣿⣤⣆⡁⢠⡿⡠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠳⠀⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⢤⢙⣯⡟⠻⣮⢄⡽⡰⢱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡷⣄⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⢯⡉⠡⠆⣌⡃⣼⣣⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡏⣸⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⡀⠀⠀⠀⠀⠀⠀⢀⠞⢠⣿⡿⠀⠀⠀⠀⢠⣦⠀⠀⢀⡤⠂⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣤⠏⣰⣿⠏⠀⠀⠀⠀⢀⡛⠄⣰⢞⣁⣴⡾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠜⢁⣾⣿⠋⣠⡴⡾⢃⣴⣬⣀⣖⣩⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⢤⠋⣠⣿⡟⣷⠿⡉⣵⡟⢻⣿⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠉⢠⣾⣿⠋⢶⢁⣾⣾⣿⡴⢿⡿⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⡁⢀⡁⣼⣿⣥⢶⣿⡾⣿⠿⣽⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣂⣵⠖⠉⢀⢈⠁⠈⠠⣿⠚⢻⣄⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⣢⠼⠖⠋⠉⣀⣤⣤⠴⠶⢿⠞⠶⢶⠿⣯⡭⣭⣭⣭⣿⣿⡏⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⢋⡉⡡⢆⣠⡴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⠈
⡠⢴⠊⣥⠄⠞⠉⣅⣰⣮⣿⠶⣾⡟⠏⠃
⡁⢀⠳⢀⣰⠶⠿⠛⠛⠂⠈⠀⠀⠁
⠡⣌⣴⠟⠁
⣿⣿⠟⠛⣿⡿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣏⣈⣷⣶⣦⣴⣶⣶⣦⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠒⠀⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⢀⠀⠀⢆⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀⡀⠀⠈⠀⠀⣄⠀⠐
⠀⠀⠀⢀⠁⢠⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠃⠀⠁⠀⠀⠐⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠑⡈⢡⡈⢹⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢳⡐⠇⠈⢦⠀⠀⠀⠈⡆⠀⠀⠀⠰⠐⠂⠀⠀⠀⡁⢀⠀⠀⠀⢀⠀⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠅⠉⠀⢸⠀⠀⠀⠀⢄⠀⠀⠀⠸⠀⢠⠀⠀⠀⠀⡀⠀⠁⢠⡈⡤⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠐⡂⠄⠀⡀⠀⠀⠊⠁⠈⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠃⠈⠀⠇⠁⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠤⢀⡀⠀⠀⠀⠀⠀⣠⠴⠁⠀⠀⠀⠀⠀⠀⠁⡠⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⢀⣀⡀⠀⡁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠄⢀⡀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢤⠤⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠄⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠂⠈⠈⠈⠉⠀⠈⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⢀⠞⡠⠃⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠝⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⡔⠣⠁⠀⠀⠀⠀⠀⠔⣠⠀⠀⠀⠠⡀⠀⠀⠀⢉⣆⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢰⢁⠀⠰⠑⢀⠀⠀⠀⠀⠀⠀⡿⡄
⠀⠀⠀⣰⠁⠃⠀⠀⠀⠀⠐⡀⠒⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠱⠀⠀⠐⠀⠀⠀⠀⣐⠛⠲⠀⢀⡀⠲⠀⢀⠁⠀⠀⠀⠀⠀⣷⣱
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡐⠀⠠⠈⠀⠀⠀⣝⠀⠀⠀⠀⢈⣁⠀⠀⠁⠀⠀⠀⠀⡏⠀⠐⠀⠀⣤⠈⢀⠍⠀⠀⠀⠀⠀⢠⠏⠛⡀
⠀⠀⠸⠃⠀⠀⠀⠀⠘⠦⠀⠀⠀⢀⠀⠀⡈⠃⠀⠀⠀⠀⠜⢨⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢨⡤⠀⠀⠀⠀⠀⠀⡌⠀⢈⡄
⠀⠀⠀⡀⠀⠀⠀⠀⣮⠁⠀⠀⢀⠀⠀⣨⠏⠀⠀⠀⠀⠜⢀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠂⠀⠉⠀⠀⠀⠀⠀⣠⠊⠀⠁⣸⠁
⠀⠀⠀⢱⠀⠀⠀⠀⠩⠄⠀⠀⢀⡄⡟⠉⠀⠀⠀⠀⠞⢀⠎⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⡁⣠⠊⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠊⠀⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠦⠀⡤⠐⢖⠘⠡⠀⡁⠠⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠤⠤⠤⢤⣤⣤⠥⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣥⣤⣀⡤⠤⠌⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⣛⣷⡶⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⣤⣶⡾⠋⢀⣠⣤⣤⣀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢠⡟⢱⡏⠀⣰⠟⢻⡆⠀⢿⠛⠶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⢿⡇⠀⣿⠛⢻⣇⠀⠻⣤⡼⠇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠦⣄⣀⣤⢼⣇⠀⢻⡄⣿⡽⢦⣄⣀⣀⣠⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⣠⡴⢿⡄⠈⢷⡄⠀⢴⣾⣿⣛⠛⠲⣽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣠⠴⠛⢁⣤⠞⠛⠶⢛⡴⠶⣄⠀⠀⠉⠳⣄⠀⠙⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⢀⡞⠁⠀⠀⠀⢸⡇⠀⠈⢳⡀⠀⠀⠙⣦⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⢹⡄⠀⠀⠈⢳⡄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⡀⠀⠀⠀⢿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢘⡇⠀⠀⠀⢸⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣿⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⣿⡇⠈⣿⠀⠀⢠⢤⡀⠀⠀⠀⡤⢄⠀⠀⠀⢀⠤⡄⠀⠀⠀⣠⢤⡀⠀⠀⠀⡤⣄⠀⠀⣽⠁⢸⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡟⢸⡇⠀⢹⡆⠀⣇⣀⡇⠀⠀⠸⣀⣨⠇⠀⠀⢮⣀⡸⠀⠀⠐⣇⣀⡇⠀⠀⢸⣀⣨⠂⢰⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡿⠀⠀⠀⠘⣇⠈⣷⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢰⡇⠀⠀⠀⠀⠘⡇⠸⣇⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠹⣆⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡄⠀⠀⠀⠀⣷⠀⠀⠙⢧⡀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⢸⡄⠀⠀⠈⠻⣦⡀⠀⠀⠈⠛⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠶⠛⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣷⣤⣄⣀⣀⣨⣿⣶⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⠛⠛⠛⠛⠛⠛⠒⠶⢤⣄⣀
⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⣶⠶⠶⠶⠶⣶
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠳⣄⠀⠼⠁⠀⣤⠀⠀⡄⠀⢠⡄⠀⠻⠄⢀⡴⠃⠀⠀⠀⢀⡟
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠳⢦⣄⣀⡁⠀⠀⠃⠀⠀⣁⣀⡤⠖⠋⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⢤⣤⣤⣤⣭⠿⠶⠶⠤⣤⣤⣤⣤⣤⣤⡤⠴⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠙⠓⠳⠦⠤⠶⠒⠛⠛⠓⠶⣤⣀⡀
⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣾⠁⣧⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⡼⠀⣷⢂⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠤⠀⣀
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⢧⢠⣇⠀⡟⢷⡄⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢠⡔⣿⣽⡀⣿⠠⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣎⣰⡏⣯⠂⣿⣿⡙⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⠀⠀⠀⠀⠀⣠⠞⠁
⣼⠀⠀⠀⠀⠀⠀⠀⠀⢾⠼⠵⢿⣼⣟⠀⣧⣻⣯⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣤⣨⡶⠋
⢰⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠐⠊⣡⡟⡆⣿⡻⢭⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠜⢋⢵⡇⡗⣿⠿⣦⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢀⢸⠁⠗⢹⠷⡬⢧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣏⠃⣻⣼⢠⣗⣏⢳⣁⣼⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢸⠿⣯⠸⣾⣗⠌⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢣⣼⣎⣼⡿⢧⡽⠃⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠙⠈⠃⠳⠘⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠠⠂
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⢀⡀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⠖⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡟⢠⣄⣀⣀⣀⠀⣀⣀⡁⣀⣀⠀⠀⢀⡎⣮⡰⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠉⠈⠈⠃⡹⠋⠉⠉⠉⠉⠁⠀⠈⠉⠀⠉⠉⠁⠁⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⡖⠀⠯⠛⠧⢽⡷⣀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣈⡉⠀⡀⠀⣠⣄⠀⠈⠐⠒⠓⣊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⡌⢳⡤⣴⢜⡛⢋⡅⠻⣖⡖⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡁⠀⠛⠋⢉⣀⠀⠻⣿⣺⡏⠑⢪⣠⡯⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⡀⣠⠶⠉⠘⠀⠀⠀⠀⠉⠀⠄⢀⠀⠉⠈⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣏⣹⡿⠖⠉⠠⠤⠠⠠⢶⣈⡓⠢⡤⠀⠤⠑⢀⠁⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠉⠉⠀⠈⠁⠀⠀⠃⠂⠙⢟⢷⡀⢀⡠⠠⣈⠉⠀⠈⠛⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⢠⠤⠠⡈⠂⠈⠳⣶⣆⣒⢾⠃
⠀⠀⠀⠀⠀⠨⡀⢠⡼⠠⠄⣠⢦⠂⠀⠊⠀⠀⠀⠠⠀⠁⠀⠀⠘⡆⢃⡈⠀⠏⢦⠀⢇⠈⠉⠉⣉⠇
⠀⠀⠀⠀⢠⠒⣿⠋⠇⠀⠀⢱⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢼⡿⠆⠒⣾⡦⠈⠛⠉⠋⢹⠀⠆
⠀⠀⠀⢠⠤⠹⢿⡴⠺⠆⠀⠐⣧⡀⠠⠀⠀⠀⠀⠀⠀⠂⠃⠀⠀⢳⣆⡀⡠⠶⠝⠦⠄⠋⠌⣿⣸⣆⣿
⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⢡⠘⢆⠈⠦⠀⠀⠄⠀⠀⡇⠀⠀⠘⠟⠇⢠⠀⠠⠄⠆⠰⠈⢙⢻⡏⡟⠑⡖⣒
⠀⠀⠀⠀⢐⡄⢘⡆⢀⠰⡂⡈⠪⠁⠈⣷⠄⠀⢤⣄⣀⡤⠰⠀⠈⢀⢠⡄⣠⠀⣠⢂⣠⣰⣦⣰⣤⠇⣥⢾⣶⡇
⠀⠀⠀⠀⠉⠉⠈⠉⠉⠁⠉⠉⠁⠈⠉⠉⠉⠉⠁⠈⠉⠈⠁⠀⠀⠉⠀⠉⠀⠉⠁⠉⠉⠘⠛⠙⠉⠉⠈⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⢻⣦⡀⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣷⣹⣇⣠⣬⣡⠴⠤⠶⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠛⠻⢿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡀
⠀⠀⠀⢸⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠠⠊⡷⠈⠓⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⢀⡽⠞⠂
⠀⠀⢀⣼⣧⣠⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⣀⣤⡷⠤⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠇⢺⣿⣶⢀
⠀⠀⢸⣿⣿⡿⠀⣰⢣⣤⣶⣟⡉⢉⡉⠁⠒⠒⠚⠛⠉⠁⠀⠀⢀⣴⣶⣶⣶⣟⣀⡙⠙⣿⣓⠦⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠻⣿⣿⡇
⠀⠀⢸⣿⣿⣷⡯⠁⠉⠀⢤⣿⣛⠻⢯⣍⡛⣶⣶⡶⠋⠀⢀⣼⣿⣿⣿⣿⡏⣏⡍⡙⠻⢦⣰⡄⠺⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⡇
⠀⠀⢸⣷⠦⣀⡀⠄⠀⠀⠘⣿⡁⠀⠀⠈⠉⠛⠟⢿⣷⣦⣿⣿⣿⣿⣿⣿⡛⠛⠿⣷⣰⣀⡉⠳⣄⠀⠑⠀⠀⠀⠀⣷⠀⣤⣿⣿⢂⣀
⠀⠀⢸⣟⢷⣄⠙⡦⡐⢥⡀⠈⠻⣷⣤⣀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣟⢿⡗⢆⣀⠉⢛⢷⣄⠘⢦⠀⠀⠄⠀⣀⣼⣷⣽⣿⣿⣿⣿⠁
⠀⠀⠀⢻⣌⠙⢿⣾⣌⡓⠀⠀⠀⠀⢹⣿⣿⣦⡀⠀⣼⣿⣿⣿⣿⣿⣿⣻⣶⣿⣦⣕⡀⣿⢿⣻⣧⠘⣇⠀⡤⢈⣿⢟⣛⣏⣹⣿⣿⠿
⠀⠀⢀⣤⣽⣷⣶⣤⣭⡉⡑⠈⠂⠈⠀⠹⣏⠈⠛⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⡹⣿⣷⡿⢿⣮⣿⣿⣿⣭⣍⡑
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⠀⠀⢹⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⢧⡏⣿⣧⣬⣱⣿⣷⣿⣿⣿⣟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡿⠃⠨⠻⠧⠔⣸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣂⣀⠿⠿⠿⠫⠭⠯⠭⣽⣭⡉⠉⠁
⠀⠀⠀⠙⣿⣿⣿⣿⣶⣾⣧⣀⣀⣀⡄⣠⠟⠴⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠂⠀⠀⠚⠒⠀⠀⠀⠈⠁
⠀⠀⠀⠠⠿⠿⢿⠿⢻⣿⠿⠋⡟⠿⣴⠿⠀⠀⢾⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⢀⣤⣤⣄
⠀⠀⠀⣠⠖⣨⣵⣾⡿⠃⠀⠈⢇⠀⠈⠛⣶⠤⢨⣉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣦⡌⠀⠀⠉
⠀⠀⠀⣡⣞⣟⣾⡟⠀⠀⠀⠀⠸⠂⠀⠈⢮⠻⣿⡻⠃⠈⠉⠹⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠁
⠀⠀⠀⣻⣿⣿⡟⣁⠀⣴⢻⣿⣷⡀⠀⠀⣠⣤⡟⠋⠀⠳⠀⠀⣠⠉⠁⠈⠙⣉⠉⠙⢻⡿⠿⠿⠿⠿⠿⠛⠛⠛⠷⠤⠀⣷⢮⢯⣤⢬⡆
⠀⠀⠀⠿⣿⣿⣥⣼⡿⠿⠿⠿⠿⠿⠆⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠩⠁⠀⠄⠌⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠄⡀⡀⢀⠀⠀⠀⠀⠀⠐⠁⢦⠄⠀⠀⠀⠁⠇⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡚⡀⠀⠀⢉⡄⠀⠀⠆⠛⡆⠠⠄⠀⠂⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣇⢒⠀⠂⠀⠀⠀⠀⠊⢤⠀⠀⡀⢆⡖⢠⢉⠄⠘⣽⡆⠃⠈⣦⠍⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣿⡽⠆⠱⠀⠀⣀⠃⠰⢆⠈⣁⠐⠈⣴⣬⢍⠞⢴⢋⢘⠐⢳⠐⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⠄⣈⣁⢀⡄⡤⠸⣂⠹⠿⢛⣧⢸⣰⣸⡻⢏⠰⢽⢉⢫⡓⣤⢆⣀⠐⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⡍⣹⡀⣤⢀⡂⢩⠰⠸⣩⣞⣩⣭⣜⡗⢋⢿⡾⣦⠶⣌⣁⠀⢼⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣝⣻⣨⣆⠿⢎⠟⢣⣅⣹⡴⣾⣿⣿⣾⣿⣿⣿⣿⡟⢀⣫⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⣧⣻⣿⣶⣛⣼⣣⣽⡗⣿⢿⣿⣿⢿⣿⣿⣿⣷⣿⣮⣿⠟⠀⠀⠀⠀⠀⢀⣀⠤⠐⠂⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣾⣯⣿⣿⣿⣷⣧⣭⣾⣿⣿⣿⣿⡿⣿⣿⢿⢿⢥⠤⡄⡲⣆⣳⣼⣿⡿⠦⣡⠞⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡏⢭⣄⠀⠉⢼⣛⡼⢾⣇⣷⠼⣽⢿⡷⠋⠉⢠⠄⠊⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡀⢘⣧⠀⠀⠈⠉⠚⠃⠐⠳⠓⠚⠛⠀⠉⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣴⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣤⣀⣀⣀⣀⣀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉




⣿⢿⠿⠿⡿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣛⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀⠄⠀⠀⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣴⣦⢀⡴⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡍⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠾⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠂⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠱⠁⠀⠀⢌⢄⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡆⠀⠂⠀⡷⠈⠆⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⡠
⠀⠀⢀⠄⠀⠐⠶⠆⠀⠀⠀⠱⠀⠀⠀⠐⠋⢧⣘⣇⣀⠁⠉⠀⠒⠠⣀⡀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠣
⠀⠀⠀⠀⠒⠰⠮⡇⠀⠀⠀⠀⠙⠤⣄⠀⠐⠀⠈⠸⠁⠀⠀⠈⠙⠂⠀⠈⠀⠀⠀⣀⡤⠚⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡷⢀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⢠⣀⣄⣠⣠⠄⠄⠰⠐⠐⠉⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠅⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡾⠀⡀⠀⠀⠀⠈⠁⢀⣴⠟⠁⠀⠀⢠⠤⡀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⣀⣈⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⡼⠁⠐⠀⠀⣀⣀⣤⣶⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣠⣾⣿⣾⣿⣿⡿⠿⠛⢻⠟⠏
⠀⠀⠀⠀⠀⠀⠀⠚⠜⠃⠀⠴⠛⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣁⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣶⣶⣶⣶⣶⣶⡶⠿⠛⠛⠋⠉
⣿⣿⡟⠛⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡆⠀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⡈⢦⠇⢰⣁⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⠠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠘⠀⠀⠀⢸
⠀⠀⡞⠓⠒⠢⠤⠤⠤⠤⡄⠀⢀⠀⢠⡀⠀⢫⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠖⠋⠢⠞⠙⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣐⠀⢀⠀⠀⠀⠐⠀⠀⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡄⠀⠀⣀⠀⠀⠠⠄⠀⠀⢉⡢⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⡀⡇
⠀⠀⠸⡐⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠂⠀⠀⠤⠀⠀⠈⠒⠀⠀⠀⠀⠀⢈⢢⠀⠀⠀⢀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠱⡡⠀⠀⠀⠂⠀⠀⠠⠃⠀⠀⠠⢂⠀⠀⠀⡄⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⡠⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠳⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠠⣠⠃
⠀⠀⠀⠀⠀⠙⢌⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⡠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣕⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣐⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠬⠥⣀⣀⣀⣀⣐⣂⣀⠩⠥⠤⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣤⢀⡤⣾⣭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣴⣿⡻⠿⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡟⠻⠋⠁
⠀⠀⣒⡫⢒⣒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⣬⣾⡿⠯⢀
⠀⠀⠀⠉⠑⠒⠫⠥⣒⣲⠤⠤⠀⣀⣀⡠⠄⠐⠒⣽⣿⠶⠎⣏⣿⣾⠳⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⢿⣁⡐⠺⢏⣱⣿⡤⣄⡾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡖⠛⠛⠛⠉⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛
⠀⠀⠀⠀⠠⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⡖⡶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⣛⡢⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣾⡿⣛⠤⢖⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢿⡿⡕⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣍⠳⠺⣌⠙⠂⢀⠀⠀⠀⠀⠀⠹⣮⢿⡌⡈⢂⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣗⠯⡢⡀⠕⢄⠀⠀⠀⠀⠹⣧⡻⡜⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⡍⢰⠀⢿⠀⠃⠀⠀⠀⠀⠀⠀⠀⣼⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⡀⢄⠑⣅⡀⠀⠀⠀⢹⣿⡜⠌⠈⠀⢀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣧⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠃⡊⠉⠀⠀⠀⠀⢯⣧⢸⡀⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣅⠠⠉⡀⠀⠀⠘⣻⠄⢇⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡿⠎⠃⢱⡇
⠀⠀⠀⠀⠀⠈⡄⢀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠈⢂⠀⠀⢣⢁⠈⡼⡄⢸⠀⠀⠀⠀⠀⠀⡰⠒⠙⠈⠋⠒⣀⠀⠀⠀⠀⢻⣃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠆⠀⠀⠀⠀⢈⡁⢰⣡⡼⠀⠀⠀⠀⠀⠀⠀⠀⢦⡼⠆⠀⢙⡀⠀⠀⠀⣸⣬⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠈⠀⠀⠈⠳⣄⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⢀⠾⠀⠀⠀⠀⣿⠟⡀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠘⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⣇⡆⢠
⠀⠀⠀⠀⠀⠀⠠⠌⠑⠰⣀⠀⠀⣤⣈⣠⣤⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣹⣵⢿⡇⢾
⠀⠀⠀⠀⠀⠀⡠⠤⠄⠀⢸⠃⢸⠏⢁⠀⠀⠙⢦⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠤⢀⡀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⣯⠀⠃⠈⡄
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠈⢺⣦⣼⡞⠉⡉⠙⠂⡤⠁⠀⣿⣿⢇⠀⠘⠀⠀⠀⢀⢐⡅⠀⡀⣠⡤⢤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⣿⢠⠀⠀⢰
⠀⠀⠀⠀⠁⢀⠀⣢⠔⠋⠉⢹⠛⣄⠀⠀⠰⣤⠁⠀⠀⣿⣿⠂⠀⠀⠀⠀⡀⠱⠉⠀⣪⠞⠁⠀⠀⠈⠻⡐⢆⠀⠀⠀⠀⠀⠀⣼⡄⡏⣸⢠⠸⢸
⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⢠⠛⣇⠈⠢⠄⠀⠘⡄⠀⠀⣿⡏⠠⠂⠀⠀⠌⣡⢈⣀⡼⠁⠀⠀⠀⠀⠀⠀⣻⠘⣰⠀⠀⠀⠀⠀⠉⡇⠣⢰⢸⠄⣾
⠀⠀⠀⠀⠀⣼⠁⠀⡰⡁⢾⠀⠙⣄⠀⠀⠀⠘⠃⠀⠀⠉⠉⠀⠀⠀⢐⠞⠃⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⠀⠀⠀⠀⠀⠀⠈⡿⣤⠈⡼⠸⡏
⠀⠀⠀⠀⠀⠸⠀⣸⠁⠀⡈⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠼⣸⢀⡟⠀⠀⠀⢠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣁⣷⠡⠁
⠀⠀⠀⠀⠀⠀⢠⣏⠀⣼⡧⠀⠠⣄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⡄⠴⠀⠏⡜⠀⠀⠀⠀⢼⣇⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⢹⣄⠀⠈⢦⣀⠐⠀⠀⠀⠀⠀⠀⠀⠘⢁⢀⢧⡄⣗⠀⠀⠀⠀⠈⢽⣾⢦⡀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⡄⠈⠈⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⢮⢸⠃⣹⡀⠀⠀⠀⠀⠈⢪⢳⡙⢦⡀⠠⠊⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢀⡿⢰⠏⠁⠀⠀⠀⠀⠀⠡⡳⣝⢦⡉⡇⢀⣤⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡳⣟⡇⢨⡁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣝⣆⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠁

⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠈⠉⠂⠠⠠⠀⠀⠀⠀⠀⠀⡄⠊⠀⠈⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠴⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⣧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⢀⠀⠐⣌⣧⠄⠀⠀⢀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠿⡦⢴⡋⡀⠀⢸⡀⠀⠀⠀⠀⠠⠾⠁⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠠⠀⠈⠑⠃⠀⠈⢱⢾⡀⣀⣸⣁⣤⣄⣀⡀⠻⣦⠐⢦⠀⢄⠀⠈⢢⡀⠀⠑⢚⢟⡽⢃⡞⡀⠀⠀⠀⠀⠀⠈⣋⡰⢀⣧⡄⠀⠀⡄
⠀⢀⡤⠴⠒⠚⠛⠋⣶⡟⢻⠋⣩⡟⠁⠀⢐⡜⣄⠈⠙⢿⠁⣺⠁⢻⢀⡦⠈⠁⠆⠀⠶⠾⠷⠉⣅⠀⠀⠀⠉⠁⠉⠉⣉⢀⣤⠃⠀⠂⠠⠄
⠀⠀⠀⠀⠢⠄⠖⠂⡨⠊⠁⢻⡟⠑⢀⣠⢯⠊⢇⡀⠀⠈⠓⠋⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⡈⣠⢀⢈⡝⠻⠿⠛⠧⣈
⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⣺⠿⠂⢠⠋⠀⠀⠀⡨⡑⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⡃⢹⠉⠀⠨⢡⡀⠐
⠀⠀⠀⠀⠄⢀⡼⠖⠓⣂⢬⢀⣀⡠⠄⠀⠀⠀⠀⠁⠘⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠺⣥⠇⠰⠐⢦⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠐⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠄⠒⠁⣹⣁⣰⠂⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠿⠩⠖⠻⡤⠿⠥⣴⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡈⠁⣰⠶⡤⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⠇⠀⠛⠀⠈⠂⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡄⠀⠰⡀⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢣⠱⣤⠟⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠄